#include <deal.II/fe/fe_nothing.h>

Inheritance diagram for FE_Nothing< dim, spacedim >:

Public Types
enum	Conformity { unknown = 0x00 , L2 = 0x01 , Hcurl = 0x02 , Hdiv = 0x04 , H1 = Hcurl \| Hdiv , H2 = 0x0e }

Public Member Functions
	FE_Nothing (const ReferenceCell &type, const unsigned int n_components=1, const bool dominate=false)

	FE_Nothing (const unsigned int n_components=1, const bool dominate=false)

virtual std::unique_ptr< FiniteElement< dim, spacedim > >	clone () const override

virtual std::string	get_name () const override

virtual UpdateFlags	requires_update_flags (const UpdateFlags update_flags) const override

virtual double	shape_value (const unsigned int i, const Point< dim > &p) const override

virtual void	fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual void	fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual void	fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase >	get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual FiniteElementDomination::Domination	compare_for_domination (const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const override final

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_vertex_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_line_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_quad_dof_identities (const FiniteElement< dim, spacedim > &fe_other, const unsigned int face_no=0) const override

virtual bool	hp_constraints_are_implemented () const override

virtual void	get_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, FullMatrix< double > &interpolation_matrix) const override

virtual void	get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, FullMatrix< double > &interpolation_matrix, const unsigned int face_no=0) const override

virtual void	get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, const unsigned int index, FullMatrix< double > &interpolation_matrix, const unsigned int face_no=0) const override

virtual std::pair< Table< 2, bool >, std::vector< unsigned int > >	get_constant_modes () const override

bool	is_dominating () const

std::pair< std::unique_ptr< FiniteElement< dim, spacedim > >, unsigned int >	operator^ (const unsigned int multiplicity) const

const FiniteElement< dim, spacedim > &	operator[] (const unsigned int fe_index) const

bool	operator== (const FiniteElementData &) const

ReferenceCell	reference_cell () const

unsigned int	n_unique_quads () const

unsigned int	n_unique_faces () const

unsigned int	n_dofs_per_vertex () const

unsigned int	n_dofs_per_line () const

unsigned int	n_dofs_per_quad (unsigned int face_no=0) const

unsigned int	max_dofs_per_quad () const

unsigned int	n_dofs_per_hex () const

unsigned int	n_dofs_per_face (unsigned int face_no=0, unsigned int child=0) const

unsigned int	max_dofs_per_face () const

unsigned int	n_dofs_per_cell () const

template<int structdim>
unsigned int	n_dofs_per_object (const unsigned int i=0) const

unsigned int	n_components () const

unsigned int	n_blocks () const

const BlockIndices &	block_indices () const

unsigned int	tensor_degree () const

bool	conforms (const Conformity) const

unsigned int	get_first_line_index () const

unsigned int	get_first_quad_index (const unsigned int quad_no=0) const

unsigned int	get_first_hex_index () const

unsigned int	get_first_face_line_index (const unsigned int face_no=0) const

unsigned int	get_first_face_quad_index (const unsigned int face_no=0) const

Shape function access
virtual double	shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 1, dim >	shape_grad (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 1, dim >	shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 2, dim >	shape_grad_grad (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 2, dim >	shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 3, dim >	shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 3, dim >	shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 4, dim >	shape_4th_derivative (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 4, dim >	shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual bool	has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const

Transfer and constraint matrices
virtual const FullMatrix< double > &	get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const

virtual const FullMatrix< double > &	get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const

bool	prolongation_is_implemented () const

bool	isotropic_prolongation_is_implemented () const

bool	restriction_is_implemented () const

bool	isotropic_restriction_is_implemented () const

bool	restriction_is_additive (const unsigned int index) const

const FullMatrix< double > &	constraints (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const

bool	constraints_are_implemented (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const

Functions to support hp-adaptivity
virtual bool	operator== (const FiniteElement< dim, spacedim > &fe) const

bool	operator!= (const FiniteElement< dim, spacedim > &) const

Index computations
std::pair< unsigned int, unsigned int >	system_to_component_index (const unsigned int index) const

unsigned int	component_to_system_index (const unsigned int component, const unsigned int index) const

std::pair< unsigned int, unsigned int >	face_system_to_component_index (const unsigned int index, const unsigned int face_no=0) const

unsigned int	adjust_quad_dof_index_for_face_orientation (const unsigned int index, const unsigned int face_no, const bool face_orientation, const bool face_flip, const bool face_rotation) const

virtual unsigned int	face_to_cell_index (const unsigned int face_dof_index, const unsigned int face, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false) const

unsigned int	adjust_line_dof_index_for_line_orientation (const unsigned int index, const bool line_orientation) const

const ComponentMask &	get_nonzero_components (const unsigned int i) const

unsigned int	n_nonzero_components (const unsigned int i) const

bool	is_primitive () const

bool	is_primitive (const unsigned int i) const

unsigned int	n_base_elements () const

virtual const FiniteElement< dim, spacedim > &	base_element (const unsigned int index) const

unsigned int	element_multiplicity (const unsigned int index) const

const FiniteElement< dim, spacedim > &	get_sub_fe (const ComponentMask &mask) const

virtual const FiniteElement< dim, spacedim > &	get_sub_fe (const unsigned int first_component, const unsigned int n_selected_components) const

std::pair< std::pair< unsigned int, unsigned int >, unsigned int >	system_to_base_index (const unsigned int index) const

std::pair< std::pair< unsigned int, unsigned int >, unsigned int >	face_system_to_base_index (const unsigned int index, const unsigned int face_no=0) const

types::global_dof_index	first_block_of_base (const unsigned int b) const

std::pair< unsigned int, unsigned int >	component_to_base_index (const unsigned int component) const

std::pair< unsigned int, unsigned int >	block_to_base_index (const unsigned int block) const

std::pair< unsigned int, types::global_dof_index >	system_to_block_index (const unsigned int component) const

unsigned int	component_to_block_index (const unsigned int component) const

Component and block matrices
ComponentMask	component_mask (const FEValuesExtractors::Scalar &scalar) const

ComponentMask	component_mask (const FEValuesExtractors::Vector &vector) const

ComponentMask	component_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const

ComponentMask	component_mask (const BlockMask &block_mask) const

BlockMask	block_mask (const FEValuesExtractors::Scalar &scalar) const

BlockMask	block_mask (const FEValuesExtractors::Vector &vector) const

BlockMask	block_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const

BlockMask	block_mask (const ComponentMask &component_mask) const

Public Attributes
const unsigned int	dofs_per_vertex

const unsigned int	dofs_per_line

const unsigned int	dofs_per_quad

const unsigned int	dofs_per_hex

const unsigned int	first_line_index

const unsigned int	first_quad_index

const unsigned int	first_hex_index

const unsigned int	first_face_line_index

const unsigned int	first_face_quad_index

const unsigned int	dofs_per_face

const unsigned int	dofs_per_cell

const unsigned int	components

const unsigned int	degree

const Conformity	conforming_space

const BlockIndices	block_indices_data

Static Public Attributes
static constexpr unsigned int	space_dimension = spacedim

static constexpr unsigned int	dimension = dim

Private Attributes
const bool	dominate

const ReferenceCell	reference_cell_kind

const unsigned int	number_unique_quads

const unsigned int	number_unique_faces

const std::vector< unsigned int >	n_dofs_on_quad

const unsigned int	dofs_per_quad_max

const std::vector< unsigned int >	first_index_of_quads

const std::vector< unsigned int >	first_line_index_of_faces

const std::vector< unsigned int >	first_quad_index_of_faces

const std::vector< unsigned int >	n_dofs_on_face

const unsigned int	dofs_per_face_max

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

void	check_no_subscribers () const noexcept

Support points and interpolation
const std::vector< Point< dim > > &	get_unit_support_points () const

bool	has_support_points () const

virtual Point< dim >	unit_support_point (const unsigned int index) const

const std::vector< Point< dim - 1 > > &	get_unit_face_support_points (const unsigned int face_no=0) const

bool	has_face_support_points (const unsigned int face_no=0) const

virtual Point< dim - 1 >	unit_face_support_point (const unsigned int index, const unsigned int face_no=0) const

const std::vector< Point< dim > > &	get_generalized_support_points () const

bool	has_generalized_support_points () const

GeometryPrimitive	get_associated_geometry_primitive (const unsigned int cell_dof_index) const

virtual void	convert_generalized_support_point_values_to_dof_values (const std::vector< Vector< double > > &support_point_values, std::vector< double > &nodal_values) const

virtual std::size_t	memory_consumption () const

std::vector< std::vector< FullMatrix< double > > >	restriction

std::vector< std::vector< FullMatrix< double > > >	prolongation

FullMatrix< double >	interface_constraints

std::vector< Point< dim > >	unit_support_points

std::vector< std::vector< Point< dim - 1 > > >	unit_face_support_points

std::vector< Point< dim > >	generalized_support_points

std::vector< std::vector< Point< dim - 1 > > >	generalized_face_support_points

std::vector< Table< 2, int > >	adjust_quad_dof_index_for_face_orientation_table

std::vector< int >	adjust_line_dof_index_for_line_orientation_table

std::vector< std::pair< unsigned int, unsigned int > >	system_to_component_table

std::vector< std::vector< std::pair< unsigned int, unsigned int > > >	face_system_to_component_table

std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > >	system_to_base_table

std::vector< std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > >	face_system_to_base_table

BlockIndices	base_to_block_indices

std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > >	component_to_base_table

const std::vector< bool >	restriction_is_additive_flags

const std::vector< ComponentMask >	nonzero_components

const std::vector< unsigned int >	n_nonzero_components_table

const bool	cached_primitivity

static ::ExceptionBase &	ExcShapeFunctionNotPrimitive (int arg1)

static ::ExceptionBase &	ExcFENotPrimitive ()

static ::ExceptionBase &	ExcUnitShapeValuesDoNotExist ()

static ::ExceptionBase &	ExcFEHasNoSupportPoints ()

static ::ExceptionBase &	ExcEmbeddingVoid ()

static ::ExceptionBase &	ExcProjectionVoid ()

static ::ExceptionBase &	ExcWrongInterfaceMatrixSize (int arg1, int arg2)

static ::ExceptionBase &	ExcInterpolationNotImplemented ()

void	reinit_restriction_and_prolongation_matrices (const bool isotropic_restriction_only=false, const bool isotropic_prolongation_only=false)

TableIndices< 2 >	interface_constraints_size () const

virtual std::unique_ptr< InternalDataBase >	get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const hp::QCollection< dim - 1 > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual std::unique_ptr< InternalDataBase >	get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim - 1 > &quadrature, internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual std::unique_ptr< InternalDataBase >	get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim - 1 > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual void	fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

virtual void	fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual void	fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual void	fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

static std::vector< unsigned int >	compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)

Detailed Description

template<int dim, int spacedim = dim>
class FE_Nothing< dim, spacedim >

Definition of a finite element space with zero degrees of freedom and that, consequently, can only represent a single function: the zero function.

This class is useful (in the context of an hp-method) to represent empty cells in the triangulation on which no degrees of freedom should be allocated, or to describe a field that is extended by zero to a part of the domain where we don't need it. Thus a triangulation may be divided into two regions: an active region where normal elements are used, and an inactive region where FE_Nothing elements are used. The DoFHandler will therefore assign no degrees of freedom to the FE_Nothing cells, and this subregion is therefore implicitly deleted from the computation. step-10 and step-46 show use cases for this element. An interesting application for this element is also presented in the paper [41].

FE_Nothing as seen as a function space

Finite elements are often best interpreted as forming a function space, i.e., a set of functions that form a vector space. One can indeed interpret FE_Nothing in this light: It corresponds to the function space \(V_h=\{0\}\), i.e., the set of functions that are zero everywhere. (The constructor can take an argument that, if greater than one, extends the space to one of vector-valued functions with more than one component, with all components equal to zero everywhere.) Indeed, this is a vector space since every linear combination of elements in the vector space is also an element in the vector space, as is every multiple of the single element zero. It is obvious that the function space has no degrees of freedom, thus the name of the class.

FE_Nothing in combination with other elements

In situations such as those of step-46, one uses FE_Nothing on cells where one is not interested in a solution variable. For example, in fluid structure interaction problems, the fluid velocity is only defined on cells inside the fluid part of the domain. One then uses FE_Nothing on cells in the solid part of the domain to describe the finite element space for the velocity. In other words, the velocity lives everywhere conceptually, but it is identically zero in those parts of the domain where it is not of interest and doesn't use up any degrees of freedom there.

The question is what happens at the interface between areas where one is interested in the solution (and uses a "normal" finite element) and where one is not interested (and uses FE_Nothing): Should the solution at that interface be zero – i.e., we consider a "continuous" finite element field that happens to be zero in that area where FE_Nothing is used – or is there no requirement for continuity at the interface. In the deal.II language, this is encoded by what the function FiniteElement::compare_for_domination() returns: If the FE_Nothing "dominates", then the solution must be zero at the interface; if it does not, then there is no requirement and one can think of FE_Nothing as a function space that is in general discontinuous (i.e., there is no requirement for any kind of continuity at cell interfaces) but on every cell equal to zero.

A constructor argument denotes whether the element should be considered dominating or not. The default is for it not to dominate, i.e., FE_Nothing is treated as a discontinuous element.

FE_Nothing in the context of hanging nodes

Note that some care must be taken that the resulting mesh topology continues to make sense when FE_Nothing elements are introduced. This is particularly true when dealing with hanging node constraints, because the library makes some basic assumptions about the nature of those constraints. The following geometries are acceptable:

+---------+----+----+
|         | 0  |    |
|    1    +----+----+
|         | 0  |    |
+---------+----+----+

+---------+----+----+
|         | 1  |    |
|    0    +----+----+
|         | 1  |    |
+---------+----+----+

Here, 0 denotes an FE_Nothing cell, and 1 denotes some other element type. The library has no difficulty computing the necessary hanging node constraints in these cases (i.e. no constraint). However, the following geometry is NOT acceptable (at least in the current implementation):

+---------+----+----+
|         | 0  |    |
|    1    +----+----+
|         | 1  |    |
+---------+----+----+

The distinction lies in the mixed nature of the child faces, a case we have not implemented as of yet.

Definition at line 129 of file fe_nothing.h.

Member Enumeration Documentation

◆ Conformity

template<int dim>

enum FiniteElementData::Conformity

inherited

Enumerator for the different types of continuity a finite element may have. Continuity is measured by the Sobolev space containing the constructed finite element space and is also called this way.

Note that certain continuities may imply others. For instance, a function in H¹ is in H^curl and H^div as well.

If you are interested in continuity in the classical sense, then the following relations hold:

H¹ implies that the function is continuous over cell boundaries.
H² implies that the function is continuously differentiable over cell boundaries.
L² indicates that the element is discontinuous. Since discontinuous elements have no topological couplings between grid cells and code may actually depend on this property, L² conformity is handled in a special way in the sense that it is not implied by any higher conformity.

In order to test if a finite element conforms to a certain space, use FiniteElementData<dim>::conforms().

Enumerator
unknown	Indicates incompatible continuities of a system.
L2	Discontinuous elements. See above!
Hcurl	Conformity with the space H^curl (continuous tangential component of a vector field)
Hdiv	Conformity with the space H^div (continuous normal component of a vector field)
H1	Conformity with the space H¹ (continuous)
H2	Conformity with the space H² (continuously differentiable)

Definition at line 259 of file fe_data.h.

Constructor & Destructor Documentation

◆ FE_Nothing() [1/2]

template<int dim, int spacedim>

FE_Nothing< dim, spacedim >::FE_Nothing	(	const ReferenceCell &	type,
		const unsigned int	n_components = `1`,
		const bool	dominate = `false`
	)

Constructor.

Parameters

[in]	type	Specifies the reference-cell type.
[in]	n_components	Denotes the number of vector components to give this finite element. The default is one.
[in]	dominate	Decides whether FE_Nothing will dominate any other FE in compare_for_domination() (with the default being `false`). Therefore at interfaces where, for example, a \(Q_1\) meets an FE_Nothing, we will force the traces of the two functions to be the same. Because the FE_Nothing encodes a space that is zero everywhere, this means that the \(Q_1\) field will be forced to become zero at this interface. See also the discussion in the general documentation of this class.

Definition at line 25 of file fe_nothing.cc.

◆ FE_Nothing() [2/2]

template<int dim, int spacedim>

FE_Nothing< dim, spacedim >::FE_Nothing	(	const unsigned int	n_components = `1`,
		const bool	dominate = `false`
	)

Same as above but for a hypercube reference-cell type.

Definition at line 52 of file fe_nothing.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< FiniteElement< dim, spacedim > > FE_Nothing< dim, spacedim >::clone ( ) const

overridevirtual

A sort of virtual copy constructor, this function returns a copy of the finite element object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FESystem as well as the hp::FECollection class, need to make copies of finite elements without knowing their exact type. They do so through this function.

Implements FiniteElement< dim, spacedim >.

Definition at line 63 of file fe_nothing.cc.

◆ get_name()

template<int dim, int spacedim>

std::string FE_Nothing< dim, spacedim >::get_name

overridevirtual

Return a string that uniquely identifies a finite element. The name is FE_Nothing<dim,spacedim>(type, n_components, dominating) where dim, spacedim, type, and n_components are all specified by the constructor or type signature with the following exceptions:

If spacedim == dim then that field is not printed.
If type is a hypercube then that field is not printed.
If n_components == 1 then that field is not printed.
If dominate == false then that field is not printed.

Implements FiniteElement< dim, spacedim >.

Definition at line 72 of file fe_nothing.cc.

◆ requires_update_flags()

template<int dim, int spacedim>

UpdateFlags FE_Nothing< dim, spacedim >::requires_update_flags ( const UpdateFlags update_flags ) const

overridevirtual

Given a set of update flags, compute which other quantities also need to be computed in order to satisfy the request by the given flags. Then return the combination of the original set of flags and those just computed.

As an example, if update_flags contains update_gradients a finite element class will typically require the computation of the inverse of the Jacobian matrix in order to rotate the gradient of shape functions on the reference cell to the real cell. It would then return not just update_gradients, but also update_covariant_transformation, the flag that makes the mapping class produce the inverse of the Jacobian matrix.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

See also: The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Implements FiniteElement< dim, spacedim >.

Definition at line 100 of file fe_nothing.cc.

◆ shape_value()

template<int dim, int spacedim>

double FE_Nothing< dim, spacedim >::shape_value	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the value of the ith shape function at the point p. p is a point on the reference element. Because the current element has no degrees of freedom, this function should obviously not be called in practice. All this function really does, therefore, is trigger an exception.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 109 of file fe_nothing.cc.

◆ fill_fe_values() [1/2]

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::fill_fe_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const CellSimilarity::Similarity	cell_similarity,
		const Quadrature< dim > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const typename FiniteElement< dim, spacedim >::InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overridevirtual

Definition at line 139 of file fe_nothing.cc.

◆ fill_fe_face_values() [1/3]

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::fill_fe_face_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const hp::QCollection< dim - 1 > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const typename FiniteElement< dim, spacedim >::InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overridevirtual

Definition at line 160 of file fe_nothing.cc.

◆ fill_fe_subface_values() [1/2]

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::fill_fe_subface_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	sub_no,
		const Quadrature< dim - 1 > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const typename FiniteElement< dim, spacedim >::InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overridevirtual

Definition at line 181 of file fe_nothing.cc.

◆ get_data()

template<int dim, int spacedim>

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > FE_Nothing< dim, spacedim >::get_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overridevirtual

Prepare internal data structures and fill in values independent of the cell. Returns a pointer to an object of which the caller of this function then has to assume ownership (which includes destruction when it is no more needed).

In the current case, this function just returns a default pointer, since no meaningful data exists for this element.

Implements FiniteElement< dim, spacedim >.

Definition at line 120 of file fe_nothing.cc.

◆ compare_for_domination()

template<int dim, int spacedim>

FiniteElementDomination::Domination FE_Nothing< dim, spacedim >::compare_for_domination	(	const FiniteElement< dim, spacedim > &	fe_other,
		const unsigned int	codim = `0`
	)		const

finaloverridevirtual

Return whether this element dominates another one given as argument fe_other, whether it is the other way around, whether neither dominates, or if either could dominate. The codim parameter describes the codimension of the investigated subspace and specifies that it is subject to this comparison. For example, if codim==0 then this function compares which element dominates at the cell level. If codim==1, then the elements are compared at faces, i.e., the comparison happens between the function spaces of the two finite elements as restricted to a face. Larger values of codim work correspondingly.

For a definition of domination, see FiniteElementDomination::Domination and in particular the hp-paper.

In the current case, this element is assumed to dominate if the second argument in the constructor dominate is true. When this argument is false and fe_other is also of type FE_Nothing(), either element can dominate. Otherwise there are no_requirements.

See also the discussion in the general documentation of this class.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 212 of file fe_nothing.cc.

◆ hp_vertex_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< dim, spacedim >::hp_vertex_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

If, on a vertex, several finite elements are active, the hp-code first assigns the degrees of freedom of each of these FEs different global indices. It then calls this function to find out which of them should get identical values, and consequently can receive the same global DoF index. This function therefore returns a list of identities between DoFs of the present finite element object with the DoFs of fe_other, which is a reference to a finite element object representing one of the other finite elements active on this particular vertex. The function computes which of the degrees of freedom of the two finite element objects are equivalent, both numbered between zero and the corresponding value of n_dofs_per_vertex() of the two finite elements. The first index of each pair denotes one of the vertex dofs of the present element, whereas the second is the corresponding index of the other finite element.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 234 of file fe_nothing.cc.

◆ hp_line_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< dim, spacedim >::hp_line_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 247 of file fe_nothing.cc.

◆ hp_quad_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< dim, spacedim >::hp_quad_dof_identities	(	const FiniteElement< dim, spacedim > &	fe_other,
		const unsigned int	face_no = `0`
	)		const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 260 of file fe_nothing.cc.

◆ hp_constraints_are_implemented()

template<int dim, int spacedim>

bool FE_Nothing< dim, spacedim >::hp_constraints_are_implemented ( ) const

overridevirtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp-compatible". That means, the element properly implements the get_face_interpolation_matrix and get_subface_interpolation_matrix methods. Therefore the return value also indicates whether a call to the get_face_interpolation_matrix() method and the get_subface_interpolation_matrix() method will generate an error or not.

Currently the main purpose of this function is to allow the make_hanging_node_constraints method to decide whether the new procedures, which are supposed to work in the hp-framework can be used, or if the old well verified but not hp-capable functions should be used. Once the transition to the new scheme for computing the interface constraints is complete, this function will be superfluous and will probably go away.

Derived classes should implement this function accordingly. The default assumption is that a finite element does not provide hp-capable face interpolation, and the default implementation therefore returns false.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 274 of file fe_nothing.cc.

◆ get_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		FullMatrix< double > &	interpolation_matrix
	)		const

overridevirtual

Return the matrix interpolating from the given finite element to the present one. Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 283 of file fe_nothing.cc.

◆ get_face_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_face_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		FullMatrix< double > &	interpolation_matrix,
		const unsigned int	face_no = `0`
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 301 of file fe_nothing.cc.

◆ get_subface_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_subface_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		const unsigned int	index,
		FullMatrix< double > &	interpolation_matrix,
		const unsigned int	face_no = `0`
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the subface of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 320 of file fe_nothing.cc.

◆ get_constant_modes()

template<int dim, int spacedim>

std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_Nothing< dim, spacedim >::get_constant_modes

overridevirtual

Return a list of constant modes of the element.

Since the current finite element has no degrees of freedom, the returned list is necessarily empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 340 of file fe_nothing.cc.

◆ is_dominating()

template<int dim, int spacedim>

bool FE_Nothing< dim, spacedim >::is_dominating

Returns: true if the FE dominates any other.

Definition at line 203 of file fe_nothing.cc.

◆ operator^()

template<int dim, int spacedim = dim>

std::pair< std::unique_ptr< FiniteElement< dim, spacedim > >, unsigned int > FiniteElement< dim, spacedim >::operator^ ( const unsigned int multiplicity ) const

inherited

Creates information for creating a FESystem with this class as base element and with multiplicity multiplicity. In particular, the return type of this function can be used in the constructor for a FESystem object. This function calls clone() and hence creates a copy of the current object.

◆ operator[]()

template<int dim, int spacedim = dim>

const FiniteElement< dim, spacedim > & FiniteElement< dim, spacedim >::operator[] ( const unsigned int fe_index ) const

inherited

This operator returns a reference to the present object if the argument given equals to zero. While this does not seem particularly useful, it is helpful in writing code that works with both DoFHandler and the hp- version hp::DoFHandler, since one can then write code like this:

dofs_per_cell =

dof_handler->get_fe()[cell->active_fe_index()].n_dofs_per_cell();

FiniteElementData::dofs_per_cell

const unsigned int dofs_per_cell

Definition: fe_data.h:433

This code doesn't work in both situations without the present operator because DoFHandler::get_fe() returns a finite element, whereas hp::DoFHandler::get_fe() returns a collection of finite elements that doesn't offer a dofs_per_cell member variable: one first has to select which finite element to work on, which is done using the operator[]. Fortunately, cell->active_fe_index() also works for non-hp-classes and simply returns zero in that case. The present operator[] accepts this zero argument, by returning the finite element with index zero within its collection (that, of course, consists only of the present finite element anyway).

Deprecated:: With DoFHandler::get_fe(int) and the deprecation of the hp::DoFHandler class, there is no more use of this operator.

◆ shape_value_component()

template<int dim, int spacedim = dim>

virtual double FiniteElement< dim, spacedim >::shape_value_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

virtualinherited

Just like for shape_value(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the value of the component-th vector component of the ith shape function at point p.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, FE_NedelecSZ< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_grad()

template<int dim, int spacedim = dim>

virtual Tensor< 1, dim > FiniteElement< dim, spacedim >::shape_grad	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

virtualinherited

Return the gradient of the ith shape function at the point p. p is a point on the reference element, and likewise the gradient is the gradient on the unit cell with respect to unit cell coordinates. If the finite element is vector-valued, then return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then derived classes implementing this function should throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_grad_component() function.

Implementations of this function should throw an exception of type ExcUnitShapeValuesDoNotExist if the shape functions of the FiniteElement under consideration depend on the shape of the cell in real space, i.e., if the shape functions are not defined by mapping from the reference cell. Some non-conforming elements are defined this way, as is the FE_DGPNonparametric class, to name just one example.

The default implementation of this virtual function does exactly this, i.e., it simply throws an exception of type ExcUnitShapeValuesDoNotExist.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, FE_NedelecSZ< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_grad_component()

template<int dim, int spacedim = dim>

virtual Tensor< 1, dim > FiniteElement< dim, spacedim >::shape_grad_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

virtualinherited

Just like for shape_grad(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component-th vector component of the ith shape function at point p.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, FE_NedelecSZ< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_grad_grad()

template<int dim, int spacedim = dim>

virtual Tensor< 2, dim > FiniteElement< dim, spacedim >::shape_grad_grad	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

virtualinherited

Return the tensor of second derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. If the finite element is vector-valued, then return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then derived classes implementing this function should throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_grad_grad_component() function.

Implementations of this function should throw an exception of type ExcUnitShapeValuesDoNotExist if the shape functions of the FiniteElement under consideration depend on the shape of the cell in real space, i.e., if the shape functions are not defined by mapping from the reference cell. Some non-conforming elements are defined this way, as is the FE_DGPNonparametric class, to name just one example.

The default implementation of this virtual function does exactly this, i.e., it simply throws an exception of type ExcUnitShapeValuesDoNotExist.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, FE_NedelecSZ< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_grad_grad_component()

template<int dim, int spacedim = dim>

virtual Tensor< 2, dim > FiniteElement< dim, spacedim >::shape_grad_grad_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

virtualinherited

Just like for shape_grad_grad(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component-th vector component of the ith shape function at point p.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, FE_NedelecSZ< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, spacedim >, FE_PolyTensor< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_3rd_derivative()

template<int dim, int spacedim = dim>

virtual Tensor< 3, dim > FiniteElement< dim, spacedim >::shape_3rd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

virtualinherited

Return the tensor of third derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. If the finite element is vector-valued, then return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then derived classes implementing this function should throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_3rd_derivative_component() function.

Implementations of this function should throw an exception of type ExcUnitShapeValuesDoNotExist if the shape functions of the FiniteElement under consideration depend on the shape of the cell in real space, i.e., if the shape functions are not defined by mapping from the reference cell. Some non-conforming elements are defined this way, as is the FE_DGPNonparametric class, to name just one example.

The default implementation of this virtual function does exactly this, i.e., it simply throws an exception of type ExcUnitShapeValuesDoNotExist.

Reimplemented in FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_3rd_derivative_component()

template<int dim, int spacedim = dim>

virtual Tensor< 3, dim > FiniteElement< dim, spacedim >::shape_3rd_derivative_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

virtualinherited

Just like for shape_3rd_derivative(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component- th vector component of the ith shape function at point p.

Reimplemented in FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_4th_derivative()

template<int dim, int spacedim = dim>

virtual Tensor< 4, dim > FiniteElement< dim, spacedim >::shape_4th_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

virtualinherited

Return the tensor of fourth derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. If the finite element is vector-valued, then return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then derived classes implementing this function should throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_4th_derivative_component() function.

Implementations of this function should throw an exception of type ExcUnitShapeValuesDoNotExist if the shape functions of the FiniteElement under consideration depend on the shape of the cell in real space, i.e., if the shape functions are not defined by mapping from the reference cell. Some non-conforming elements are defined this way, as is the FE_DGPNonparametric class, to name just one example.

The default implementation of this virtual function does exactly this, i.e., it simply throws an exception of type ExcUnitShapeValuesDoNotExist.

Reimplemented in FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ shape_4th_derivative_component()

template<int dim, int spacedim = dim>

virtual Tensor< 4, dim > FiniteElement< dim, spacedim >::shape_4th_derivative_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

virtualinherited

Just like for shape_4th_derivative(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component- th vector component of the ith shape function at point p.

Reimplemented in FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ has_support_on_face()

template<int dim, int spacedim = dim>

virtual bool FiniteElement< dim, spacedim >::has_support_on_face	(	const unsigned int	shape_index,
		const unsigned int	face_index
	)		const

virtualinherited

This function returns true, if the shape function shape_index has non-zero function values somewhere on the face face_index. The function is typically used to determine whether some matrix elements resulting from face integrals can be assumed to be zero and may therefore be omitted from integration.

A default implementation is provided in this base class which always returns true. This is the safe way to go.

◆ get_restriction_matrix()

template<int dim, int spacedim = dim>

virtual const FullMatrix< double > & FiniteElement< dim, spacedim >::get_restriction_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase< dim >::isotropic_refinement`
	)		const

virtualinherited

Return the matrix that describes restricting a finite element field from the given child (as obtained by the given refinement_case) to the parent cell. The interpretation of the returned matrix depends on what restriction_is_additive() returns for each shape function.

Row and column indices are related to coarse grid and fine grid spaces, respectively, consistent with the definition of the associated operator.

If projection matrices are not implemented in the derived finite element class, this function aborts with an exception of type FiniteElement::ExcProjectionVoid. You can check whether this would happen by first calling the restriction_is_implemented() or the isotropic_restriction_is_implemented() function.

Reimplemented in FE_Q_Bubbles< dim, spacedim >, FE_Bernstein< dim, spacedim >, FE_DGQ< dim, spacedim >, FE_DGQ< dim, dim >, FE_Enriched< dim, spacedim >, FE_Nedelec< dim >, FE_Q_Base< dim, spacedim >, FE_Q_Base< dim, dim >, FE_Q_Base< dim, spacedim >, FE_RaviartThomasNodal< dim >, FE_SimplexPoly< dim, spacedim >, FE_SimplexPoly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ get_prolongation_matrix()

template<int dim, int spacedim = dim>

virtual const FullMatrix< double > & FiniteElement< dim, spacedim >::get_prolongation_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase< dim >::isotropic_refinement`
	)		const

virtualinherited

Prolongation/embedding matrix between grids.

The identity operator from a coarse grid space into a fine grid space (where both spaces are identified as functions defined on the parent and child cells) is associated with a matrix P that maps the corresponding representations of these functions in terms of their nodal values. The restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation, not the sum of the cell matrices P_i. That is, if the same non-zero entry j,k exists in two different child matrices P_i, the value should be the same in both matrices and it is copied into the matrix P only once.

Row and column indices are related to fine grid and coarse grid spaces, respectively, consistent with the definition of the associated operator.

These matrices are used by routines assembling the prolongation matrix for multi-level methods. Upon assembling the transfer matrix between cells using this matrix array, zero elements in the prolongation matrix are discarded and will not fill up the transfer matrix.

If prolongation matrices are not implemented in the derived finite element class, this function aborts with an exception of type FiniteElement::ExcEmbeddingVoid. You can check whether this would happen by first calling the prolongation_is_implemented() or the isotropic_prolongation_is_implemented() function.

Reimplemented in FE_Q_Bubbles< dim, spacedim >, FE_Bernstein< dim, spacedim >, FE_DGQ< dim, spacedim >, FE_DGQ< dim, dim >, FE_Enriched< dim, spacedim >, FE_Nedelec< dim >, FE_Q_Base< dim, spacedim >, FE_Q_Base< dim, dim >, FE_Q_Base< dim, spacedim >, FE_Q_Hierarchical< dim >, FE_RaviartThomasNodal< dim >, FE_SimplexPoly< dim, spacedim >, FE_SimplexPoly< dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ prolongation_is_implemented()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::prolongation_is_implemented ( ) const

inherited

Return whether this element implements its prolongation matrices. The return value also indicates whether a call to the get_prolongation_matrix() function will generate an error or not.

Note, that this function returns true only if the prolongation matrices of the isotropic and all anisotropic refinement cases are implemented. If you are interested in the prolongation matrices for isotropic refinement only, use the isotropic_prolongation_is_implemented function instead.

This function is mostly here in order to allow us to write more efficient test programs which we run on all kinds of weird elements, and for which we simply need to exclude certain tests in case something is not implemented. It will in general probably not be a great help in applications, since there is not much one can do if one needs these features and they are not implemented. This function could be used to check whether a call to get_prolongation_matrix() will succeed; however, one then still needs to cope with the lack of information this just expresses.

◆ isotropic_prolongation_is_implemented()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::isotropic_prolongation_is_implemented ( ) const

inherited

Return whether this element implements its prolongation matrices for isotropic children. The return value also indicates whether a call to the get_prolongation_matrix function will generate an error or not.

This function is mostly here in order to allow us to write more efficient test programs which we run on all kinds of weird elements, and for which we simply need to exclude certain tests in case something is not implemented. It will in general probably not be a great help in applications, since there is not much one can do if one needs these features and they are not implemented. This function could be used to check whether a call to get_prolongation_matrix() will succeed; however, one then still needs to cope with the lack of information this just expresses.

◆ restriction_is_implemented()

template<int dim, int spacedim = dim>

This covers most cases where elements can differ, but there are cases of derived elements that are different and for which the current function still returns true. For these cases, derived classes should overload this function.

Note

This operator specifically does not check the following member variables of the current class:

restriction matrices,
prolongation matrices of this object and the argument. This is because these member variables may be initialized only on demand by derived classes, rather than being available immediately. Consequently, comparing these members would not only be costly because these are generally big arrays, but also because their computation may be expensive. On the other hand, derived classes for which these arrays may differ for two objects even though the above list compares as equal, will probably want to implement their own operator==() anyway.

◆ operator==() [2/2]

template<int dim>

bool FiniteElementData< dim >::operator== ( const FiniteElementData< dim > & f ) const

inherited

Comparison operator.

Definition at line 196 of file fe_data.cc.

◆ operator!=()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::operator!= ( const FiniteElement< dim, spacedim > & ) const

inherited

Non-equality comparison operator. Defined in terms of the equality comparison operator.

◆ system_to_component_index()

template<int dim, int spacedim = dim>

std::pair< unsigned int, unsigned int > FiniteElement< dim, spacedim >::system_to_component_index ( const unsigned int index ) const

inherited

Compute vector component and index of this shape function within the shape functions corresponding to this component from the index of a shape function within this finite element.

If the element is scalar, then the component is always zero, and the index within this component is equal to the overall index.

If the shape function referenced has more than one non-zero component, then it cannot be associated with one vector component, and an exception of type ExcShapeFunctionNotPrimitive will be raised.

Note that if the element is composed of other (base) elements, and a base element has more than one component but all its shape functions are primitive (i.e. are non-zero in only one component), then this mapping contains valid information. However, the index of a shape function of this element within one component (i.e. the second number of the respective entry of this array) does not indicate the index of the respective shape function within the base element (since that has more than one vector-component). For this information, refer to the system_to_base_table field and the system_to_base_index() function.

See the class description above for an example of how this function is typically used.

The use of this function is explained extensively in the step-8 and step-20 tutorial programs as well as in the Handling vector valued problems module.

◆ component_to_system_index()

template<int dim, int spacedim = dim>

unsigned int FiniteElement< dim, spacedim >::component_to_system_index	(	const unsigned int	component,
		const unsigned int	index
	)		const

inherited

Compute the shape function for the given vector component and index.

If the element is scalar, then the component must be zero, and the index within this component is equal to the overall index.

This is the opposite operation from the system_to_component_index() function.

◆ face_system_to_component_index()

template<int dim, int spacedim = dim>

std::pair< unsigned int, unsigned int > FiniteElement< dim, spacedim >::face_system_to_component_index	(	const unsigned int	index,
		const unsigned int	face_no = `0`
	)		const

inherited

Same as system_to_component_index(), but do it for shape functions and their indices on a face. The range of allowed indices is therefore 0..dofs_per_face.

You will rarely need this function in application programs, since almost all application codes only need to deal with cell indices, not face indices. The function is mainly there for use inside the library.

◆ adjust_quad_dof_index_for_face_orientation()

template<int dim, int spacedim = dim>

unsigned int FiniteElement< dim, spacedim >::adjust_quad_dof_index_for_face_orientation	(	const unsigned int	index,
		const unsigned int	face_no,
		const bool	face_orientation,
		const bool	face_flip,
		const bool	face_rotation
	)		const

inherited

For faces with non-standard face_orientation in 3D, the dofs on faces (quads) have to be permuted in order to be combined with the correct shape functions. Given a local dof index on a quad, return the local index, if the face has non-standard face_orientation, face_flip or face_rotation. In 2D and 1D there is no need for permutation and consequently an exception is thrown.

◆ face_to_cell_index()

template<int dim, int spacedim = dim>

virtual unsigned int FiniteElement< dim, spacedim >::face_to_cell_index	(	const unsigned int	face_dof_index,
		const unsigned int	face,
		const bool	face_orientation = `true`,
		const bool	face_flip = `false`,
		const bool	face_rotation = `false`
	)		const

virtualinherited

Given an index in the natural ordering of indices on a face, return the index of the same degree of freedom on the cell.

To explain the concept, consider the case where we would like to know whether a degree of freedom on a face, for example as part of an FESystem element, is primitive. Unfortunately, the is_primitive() function in the FiniteElement class takes a cell index, so we would need to find the cell index of the shape function that corresponds to the present face index. This function does that.

Code implementing this would then look like this:

for (i=0; i<dofs_per_face; ++i)
 if (fe.is_primitive(fe.face_to_cell_index(i, some_face_no)))
  ... do whatever

The function takes additional arguments that account for the fact that actual faces can be in their standard ordering with respect to the cell under consideration, or can be flipped, oriented, etc.

Parameters

face_dof_index	The index of the degree of freedom on a face. This index must be between zero and dofs_per_face.
face	The number of the face this degree of freedom lives on. This number must be between zero and GeometryInfo::faces_per_cell.
face_orientation	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_flip	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_rotation	One part of the description of the orientation of the face. See GlossFaceOrientation.

Returns: The index of this degree of freedom within the set of degrees of freedom on the entire cell. The returned value will be between zero and dofs_per_cell.

Note: This function exists in this class because that is where it was first implemented. However, it can't really work in the most general case without knowing what element we have. The reason is that when a face is flipped or rotated, we also need to know whether we need to swap the degrees of freedom on this face, or whether they are immune from this. For this, consider the situation of a \(Q_3\) element in 2d. If face_flip is true, then we need to consider the two degrees of freedom on the edge in reverse order. On the other hand, if the element were a \(Q_1^2\), then because the two degrees of freedom on this edge belong to different vector components, they should not be considered in reverse order. What all of this shows is that the function can't work if there are more than one degree of freedom per line or quad, and that in these cases the function will throw an exception pointing out that this functionality will need to be provided by a derived class that knows what degrees of freedom actually represent.

Reimplemented in FE_Q_Base< dim, spacedim >, FE_Q_Base< dim, dim >, FE_Q_Base< dim, spacedim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ adjust_line_dof_index_for_line_orientation()

template<int dim, int spacedim = dim>

unsigned int FiniteElement< dim, spacedim >::adjust_line_dof_index_for_line_orientation	(	const unsigned int	index,
		const bool	line_orientation
	)		const

inherited

For lines with non-standard line_orientation in 3D, the dofs on lines have to be permuted in order to be combined with the correct shape functions. Given a local dof index on a line, return the local index, if the line has non-standard line_orientation. In 2D and 1D there is no need for permutation, so the given index is simply returned.

◆ get_nonzero_components()

template<int dim, int spacedim = dim>

template<int dim, int spacedim = dim>

unsigned int FiniteElement< dim, spacedim >::element_multiplicity ( const unsigned int index ) const

inherited

This index denotes how often the base element index is used in a composed element. If the element is atomic, then the result is always equal to one. See the documentation for the n_base_elements() function for more details.

◆ get_sub_fe() [1/2]

template<int dim, int spacedim = dim>

const FiniteElement< dim, spacedim > & FiniteElement< dim, spacedim >::get_sub_fe ( const ComponentMask & mask ) const

inherited

Return a reference to a contained finite element that matches the components selected by the given ComponentMask mask.

For an arbitrarily nested FESystem, this function returns the inner-most FiniteElement that matches the given mask. The method fails if the mask does not exactly match one of the contained finite elements. It is most useful if the current object is an FESystem, as the return value can only be this in all other cases.

Note that the returned object can be an FESystem if the mask matches it but not any of the contained objects.

Let us illustrate the function with the an FESystem fe with 7 components:

FESystem<2> fe_velocity(FE_Q<2>(2), 2);
FE_Q<2> fe_pressure(1);
FE_DGP<2> fe_dg(0);
FE_BDM<2> fe_nonprim(1);
FESystem<2> fe(fe_velocity, 1, fe_pressure, 1, fe_dg, 2, fe_nonprim, 1);

The following table lists all possible component masks you can use:

ComponentMask	Result	Description
`[true,true,true,true,true,true,true]`	`FESystem<2>[FESystem<2>[FE_Q<2>(2)^2]-FE_Q<2>(1)-FE_DGP<2>(0)^2-FE_BDM<2>(1)]`	`fe` itself, the whole `FESystem`
`[true,true,false,false,false,false,false]`	`FESystem<2>[FE_Q<2>(2)^2]`	just the `fe_velocity`
`[true,false,false,false,false,false,false]`	`FE_Q<2>(2)`	The first component in `fe_velocity`
`[false,true,false,false,false,false,false]`	`FE_Q<2>(2)`	The second component in `fe_velocity`
`[false,false,true,false,false,false,false]`	`FE_Q<2>(1)`	`fe_pressure`
`[false,false,false,true,false,false,false]`	`FE_DGP<2>(0)`	first copy of `fe_dg`
`[false,false,false,false,true,false,false]`	`FE_DGP<2>(0)`	second copy of `fe_dg`
`[false,false,false,false,false,true,true]`	`FE_BDM<2>(1)`	both components of `fe_nonprim`

◆ get_sub_fe() [2/2]

template<int dim, int spacedim = dim>

virtual const FiniteElement< dim, spacedim > & FiniteElement< dim, spacedim >::get_sub_fe	(	const unsigned int	first_component,
		const unsigned int	n_selected_components
	)		const

virtualinherited

Return a reference to a contained finite element that matches the components n_selected_components components starting at component with index first_component.

See the other get_sub_fe() function above for more details.

Reimplemented in FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ system_to_base_index()

template<int dim, int spacedim = dim>

std::pair< std::pair< unsigned int, unsigned int >, unsigned int > FiniteElement< dim, spacedim >::system_to_base_index ( const unsigned int index ) const

inherited

Return for shape function index the base element it belongs to, the number of the copy of this base element (which is between zero and the multiplicity of this element), and the index of this shape function within this base element.

If the element is not composed of others, then base and instance are always zero, and the index is equal to the number of the shape function. If the element is composed of single instances of other elements (i.e. all with multiplicity one) all of which are scalar, then base values and dof indices within this element are equal to the system_to_component_table. It differs only in case the element is composed of other elements and at least one of them is vector-valued itself.

See the class documentation above for an example of how this function is typically used.

This function returns valid values also in the case of vector-valued (i.e. non-primitive) shape functions, in contrast to the system_to_component_index() function.

◆ face_system_to_base_index()

template<int dim, int spacedim = dim>

std::pair< std::pair< unsigned int, unsigned int >, unsigned int > FiniteElement< dim, spacedim >::face_system_to_base_index	(	const unsigned int	index,
		const unsigned int	face_no = `0`
	)		const

inherited

Same as system_to_base_index(), but for degrees of freedom located on a face. The range of allowed indices is therefore 0..dofs_per_face.

You will rarely need this function in application programs, since almost all application codes only need to deal with cell indices, not face indices. The function is mainly there for use inside the library.

◆ first_block_of_base()

template<int dim, int spacedim = dim>

types::global_dof_index FiniteElement< dim, spacedim >::first_block_of_base ( const unsigned int b ) const

inherited

Given a base element number, return the first block of a BlockVector it would generate.

◆ component_to_base_index()

template<int dim, int spacedim = dim>

std::pair< unsigned int, unsigned int > FiniteElement< dim, spacedim >::component_to_base_index ( const unsigned int component ) const

inherited

For each vector component, return which base element implements this component and which vector component in this base element this is. This information is only of interest for vector-valued finite elements which are composed of several sub-elements. In that case, one may want to obtain information about the element implementing a certain vector component, which can be done using this function and the FESystem::base_element() function.

If this is a scalar finite element, then the return value is always equal to a pair of zeros.

◆ block_to_base_index()

template<int dim, int spacedim = dim>

std::pair< unsigned int, unsigned int > FiniteElement< dim, spacedim >::block_to_base_index ( const unsigned int block ) const

inherited

Return the base element for this block and the number of the copy of the base element.

◆ system_to_block_index()

template<int dim, int spacedim = dim>

std::pair< unsigned int, types::global_dof_index > FiniteElement< dim, spacedim >::system_to_block_index ( const unsigned int component ) const

inherited

The vector block and the index inside the block for this shape function.

◆ component_to_block_index()

template<int dim, int spacedim = dim>

unsigned int FiniteElement< dim, spacedim >::component_to_block_index ( const unsigned int component ) const

inherited

The vector block for this component.

◆ component_mask() [1/4]

template<int dim, int spacedim = dim>

ComponentMask FiniteElement< dim, spacedim >::component_mask ( const FEValuesExtractors::Scalar & scalar ) const

inherited

Return a component mask with as many elements as this object has vector components and of which exactly the one component is true that corresponds to the given argument. See the glossary for more information.

Parameters

scalar An object that represents a single scalar vector component of this finite element.

Returns: A component mask that is false in all components except for the one that corresponds to the argument.

◆ component_mask() [2/4]

template<int dim, int spacedim = dim>

ComponentMask FiniteElement< dim, spacedim >::component_mask ( const FEValuesExtractors::Vector & vector ) const

inherited

Return a component mask with as many elements as this object has vector components and of which exactly the dim components are true that correspond to the given argument. See the glossary for more information.

Parameters

vector An object that represents dim vector components of this finite element.

Returns: A component mask that is false in all components except for the ones that corresponds to the argument.

◆ component_mask() [3/4]

template<int dim, int spacedim = dim>

ComponentMask FiniteElement< dim, spacedim >::component_mask ( const FEValuesExtractors::SymmetricTensor< 2 > & sym_tensor ) const

inherited

Return a component mask with as many elements as this object has vector components and of which exactly the dim*(dim+1)/2 components are true that correspond to the given argument. See the glossary for more information.

Parameters

sym_tensor An object that represents dim*(dim+1)/2 components of this finite element that are jointly to be interpreted as forming a symmetric tensor.

Returns: A component mask that is false in all components except for the ones that corresponds to the argument.

◆ component_mask() [4/4]

template<int dim, int spacedim = dim>

ComponentMask FiniteElement< dim, spacedim >::component_mask ( const BlockMask & block_mask ) const

inherited

Given a block mask (see this glossary entry), produce a component mask (see this glossary entry) that represents the components that correspond to the blocks selected in the input argument. This is essentially a conversion operator from BlockMask to ComponentMask.

Parameters

block_mask The mask that selects individual blocks of the finite element

Returns: A mask that selects those components corresponding to the selected blocks of the input argument.

◆ block_mask() [1/4]

template<int dim, int spacedim = dim>

BlockMask FiniteElement< dim, spacedim >::block_mask ( const FEValuesExtractors::Scalar & scalar ) const

inherited

Return a block mask with as many elements as this object has blocks and of which exactly the one component is true that corresponds to the given argument. See the glossary for more information.

Note: This function will only succeed if the scalar referenced by the argument encompasses a complete block. In other words, if, for example, you pass an extractor for the single \(x\) velocity and this object represents an FE_RaviartThomas object, then the single scalar object you selected is part of a larger block and consequently there is no block mask that would represent it. The function will then produce an exception.

Parameters

scalar An object that represents a single scalar vector component of this finite element.

Returns: A component mask that is false in all components except for the one that corresponds to the argument.

◆ block_mask() [2/4]

template<int dim, int spacedim = dim>

BlockMask FiniteElement< dim, spacedim >::block_mask ( const FEValuesExtractors::Vector & vector ) const

inherited

Return a component mask with as many elements as this object has vector components and of which exactly the dim components are true that correspond to the given argument. See the glossary for more information.

Note: The same caveat applies as to the version of the function above: The extractor object passed as argument must be so that it corresponds to full blocks and does not split blocks of this element.

Parameters

vector An object that represents dim vector components of this finite element.

Returns: A component mask that is false in all components except for the ones that corresponds to the argument.

◆ block_mask() [3/4]

template<int dim, int spacedim = dim>

BlockMask FiniteElement< dim, spacedim >::block_mask ( const FEValuesExtractors::SymmetricTensor< 2 > & sym_tensor ) const

inherited

Return a component mask with as many elements as this object has vector components and of which exactly the dim*(dim+1)/2 components are true that correspond to the given argument. See the glossary for more information.

Note: The same caveat applies as to the version of the function above: The extractor object passed as argument must be so that it corresponds to full blocks and does not split blocks of this element.

Parameters

sym_tensor An object that represents dim*(dim+1)/2 components of this finite element that are jointly to be interpreted as forming a symmetric tensor.

Returns: A component mask that is false in all components except for the ones that corresponds to the argument.

◆ block_mask() [4/4]

template<int dim, int spacedim = dim>

BlockMask FiniteElement< dim, spacedim >::block_mask ( const ComponentMask & component_mask ) const

inherited

Given a component mask (see this glossary entry), produce a block mask (see this glossary entry) that represents the blocks that correspond to the components selected in the input argument. This is essentially a conversion operator from ComponentMask to BlockMask.

Note: This function will only succeed if the components referenced by the argument encompasses complete blocks. In other words, if, for example, you pass an component mask for the single \(x\) velocity and this object represents an FE_RaviartThomas object, then the single component you selected is part of a larger block and consequently there is no block mask that would represent it. The function will then produce an exception.

Parameters

component_mask The mask that selects individual components of the finite element

Returns: A mask that selects those blocks corresponding to the selected blocks of the input argument.

◆ get_unit_support_points()

template<int dim, int spacedim = dim>

const std::vector< Point< dim > > & FiniteElement< dim, spacedim >::get_unit_support_points ( ) const

inherited

Return the support points of the trial functions on the unit cell, if the derived finite element defines them. Finite elements that allow some kind of interpolation operation usually have support points. On the other hand, elements that define their degrees of freedom by, for example, moments on faces, or as derivatives, don't have support points. In that case, the returned field is empty.

If the finite element defines support points, then their number equals the number of degrees of freedom of the element. The order of points in the array matches that returned by the cell->get_dof_indices function.

See the class documentation for details on support points.

Note: Finite elements' implementation of this function returns these points in the same order as shape functions. The order of shape functions is typically documented in the class documentation of the various finite element classes. In particular, shape functions (and consequently the mapped quadrature points discussed in the class documentation of this class) will then traverse first those shape functions located on vertices, then on lines, then on quads, etc.; If this element implements support points, then it will return one such point per shape function. Since multiple shape functions may be defined at the same location, the support points returned here may be duplicated. An example would be an element of the kind FESystem(FE_Q(1),3) for which each support point would appear three times in the returned array.

◆ has_support_points()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::has_support_points ( ) const

inherited

Return whether a finite element has defined support points. If the result is true, then a call to the get_unit_support_points() yields a non-empty array.

The result may be false if an element is not defined by interpolating shape functions, for example by P-elements on quadrilaterals. It will usually only be true if the element constructs its shape functions by the requirement that they be one at a certain point and zero at all the points associated with the other shape functions.

In composed elements (i.e. for the FESystem class), the result will be true if all the base elements have defined support points. FE_Nothing is a special case in FESystems, because it has 0 support points and has_support_points() is false, but an FESystem containing an FE_Nothing among other elements will return true.

◆ unit_support_point()

template<int dim, int spacedim = dim>

virtual Point< dim > FiniteElement< dim, spacedim >::unit_support_point ( const unsigned int index ) const

virtualinherited

Return the position of the support point of the indexth shape function. If it does not exist, raise an exception.

The default implementation simply returns the respective element from the array you get from get_unit_support_points(), but derived elements may overload this function. In particular, note that the FESystem class overloads it so that it can return the support points of individual base elements, if not all the base elements define support points. In this way, you can still ask for certain support points, even if get_unit_support_points() only returns an empty array.

Reimplemented in FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ get_unit_face_support_points()

template<int dim, int spacedim = dim>

const std::vector< Point< dim - 1 > > & FiniteElement< dim, spacedim >::get_unit_face_support_points ( const unsigned int face_no = 0 ) const

inherited

Return the support points of the trial functions on the unit face, if the derived finite element defines some. Finite elements that allow some kind of interpolation operation usually have support points. On the other hand, elements that define their degrees of freedom by, for example, moments on faces, or as derivatives, don't have support points. In that case, the returned field is empty

Note that elements that have support points need not necessarily have some on the faces, even if the interpolation points are located physically on a face. For example, the discontinuous elements have interpolation points on the vertices, and for higher degree elements also on the faces, but they are not defined to be on faces since in that case degrees of freedom from both sides of a face (or from all adjacent elements to a vertex) would be identified with each other, which is not what we would like to have). Logically, these degrees of freedom are therefore defined to belong to the cell, rather than the face or vertex. In that case, the returned element would therefore have length zero.

If the finite element defines support points, then their number equals the number of degrees of freedom on the face (dofs_per_face). The order of points in the array matches that returned by the cell->face(face)->get_dof_indices function.

See the class documentation for details on support points.

◆ has_face_support_points()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::has_face_support_points ( const unsigned int face_no = 0 ) const

inherited

Return whether a finite element has defined support points on faces. If the result is true, then a call to the get_unit_face_support_points() yields a non-empty vector.

For more information, see the documentation for the has_support_points() function.

◆ unit_face_support_point()

template<int dim, int spacedim = dim>

virtual Point< dim - 1 > FiniteElement< dim, spacedim >::unit_face_support_point	(	const unsigned int	index,
		const unsigned int	face_no = `0`
	)		const

virtualinherited

The function corresponding to the unit_support_point() function, but for faces. See there for more information.

Reimplemented in FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ get_generalized_support_points()

template<int dim, int spacedim = dim>

const std::vector< Point< dim > > & FiniteElement< dim, spacedim >::get_generalized_support_points ( ) const

inherited

Return a vector of generalized support points.

Note: The vector returned by this function is always a minimal set of unique support points. This is in contrast to the behavior of get_unit_support_points() that returns a repeated list of unit support points for an FESystem of numerous (Lagrangian) base elements.

See the glossary entry on generalized support points for more information.

◆ has_generalized_support_points()

template<int dim, int spacedim = dim>

bool FiniteElement< dim, spacedim >::has_generalized_support_points ( ) const

inherited

Return whether a finite element has defined generalized support points. If the result is true, then a call to the get_generalized_support_points() yields a non-empty vector.

See the glossary entry on generalized support points for more information.

◆ get_associated_geometry_primitive()

template<int dim, int spacedim = dim>

GeometryPrimitive FiniteElement< dim, spacedim >::get_associated_geometry_primitive ( const unsigned int cell_dof_index ) const

inherited

For a given degree of freedom, return whether it is logically associated with a vertex, line, quad or hex.

For instance, for continuous finite elements this coincides with the lowest dimensional object the support point of the degree of freedom lies on. To give an example, for \(Q_1\) elements in 3d, every degree of freedom is defined by a shape function that we get by interpolating using support points that lie on the vertices of the cell. The support of these points of course extends to all edges connected to this vertex, as well as the adjacent faces and the cell interior, but we say that logically the degree of freedom is associated with the vertex as this is the lowest- dimensional object it is associated with. Likewise, for \(Q_2\) elements in 3d, the degrees of freedom with support points at edge midpoints would yield a value of GeometryPrimitive::line from this function, whereas those on the centers of faces in 3d would return GeometryPrimitive::quad.

To make this more formal, the kind of object returned by this function represents the object so that the support of the shape function corresponding to the degree of freedom, (i.e., that part of the domain where the function "lives") is the union of all of the cells sharing this object. To return to the example above, for \(Q_2\) in 3d, the shape function with support point at an edge midpoint has support on all cells that share the edge and not only the cells that share the adjacent faces, and consequently the function will return GeometryPrimitive::line.

On the other hand, for discontinuous elements of type \(DGQ_2\), a degree of freedom associated with an interpolation polynomial that has its support point physically located at a line bounding a cell, but is nonzero only on one cell. Consequently, it is logically associated with the interior of that cell (i.e., with a GeometryPrimitive::quad in 2d and a GeometryPrimitive::hex in 3d).

Parameters

[in] cell_dof_index The index of a shape function or degree of freedom. This index must be in the range [0,dofs_per_cell).

Note: The integer value of the object returned by this function equals the dimensionality of the object it describes, and can consequently be used in generic programming paradigms. For example, if a degree of freedom is associated with a vertex, then this function returns GeometryPrimitive::vertex, which has a numeric value of zero (the dimensionality of a vertex).

◆ convert_generalized_support_point_values_to_dof_values()

template<int dim, int spacedim = dim>

virtual void FiniteElement< dim, spacedim >::convert_generalized_support_point_values_to_dof_values	(	const std::vector< Vector< double > > &	support_point_values,
		std::vector< double > &	nodal_values
	)		const

virtualinherited

Given the values of a function \(f(\mathbf x)\) at the (generalized) support points of the reference cell, this function then computes what the nodal values of the element are, i.e., \(\Psi_i[f]\), where \(\Psi_i\) are the node functionals of the element (see also Node values or node functionals). The values \(\Psi_i[f]\) are then the expansion coefficients for the shape functions of the finite element function that interpolates the given function \(f(x)\), i.e., \( f_h(\mathbf x) = \sum_i \Psi_i[f] \varphi_i(\mathbf x) \) is the finite element interpolant of \(f\) with the current element. The operation described here is used, for example, in the FETools::compute_node_matrix() function.

In more detail, let us assume that the generalized support points (see this glossary entry ) of the current element are \(\hat{\mathbf x}_i\) and that the node functionals associated with the current element are \(\Psi_i[\cdot]\). Then, the fact that the element is based on generalized support points, implies that if we apply \(\Psi_i\) to a (possibly vector-valued) finite element function \(\varphi\), the result must have the form \(\Psi_i[\varphi] = f_i(\varphi(\hat{\mathbf x}_i))\) – in other words, the value of the node functional \(\Psi_i\) applied to \(\varphi\) only depends on the values of \(\varphi\) at \(\hat{\mathbf x}_i\) and not on values anywhere else, or integrals of \(\varphi\), or any other kind of information.

The exact form of \(f_i\) depends on the element. For example, for scalar Lagrange elements, we have that in fact \(\Psi_i[\varphi] = \varphi(\hat{\mathbf x}_i)\). If you combine multiple scalar Lagrange elements via an FESystem object, then \(\Psi_i[\varphi] = \varphi(\hat{\mathbf x}_i)_{c(i)}\) where \(c(i)\) is the result of the FiniteElement::system_to_component_index() function's return value's first component. In these two cases, \(f_i\) is therefore simply the identity (in the scalar case) or a function that selects a particular vector component of its argument. On the other hand, for Raviart-Thomas elements, one would have that \(f_i(\mathbf y) = \mathbf y \cdot \mathbf n_i\) where \(\mathbf n_i\) is the normal vector of the face at which the shape function is defined.

Given all of this, what this function does is the following: If you input a list of values of a function \(\varphi\) at all generalized support points (where each value is in fact a vector of values with as many components as the element has), then this function returns a vector of values obtained by applying the node functionals to these values. In other words, if you pass in \(\{\varphi(\hat{\mathbf x}_i)\}_{i=0}^{N-1}\) then you will get out a vector \(\{\Psi[\varphi]\}_{i=0}^{N-1}\) where \(N\) equals dofs_per_cell.

Parameters

[in]	support_point_values	An array of size `dofs_per_cell` (which equals the number of points the get_generalized_support_points() function will return) where each element is a vector with as many entries as the element has vector components. This array should contain the values of a function at the generalized support points of the current element.
[out]	nodal_values	An array of size `dofs_per_cell` that contains the node functionals of the element applied to the given function.

Note: It is safe to call this function for (transformed) values on the real cell only for elements with trivial MappingKind. For all other elements (for example for H(curl), or H(div) conforming elements) vector values have to be transformed to the reference cell first.; Given what the function is supposed to do, the function clearly can only work for elements that actually implement (generalized) support points. Elements that do not have generalized support points – e.g., elements whose nodal functionals evaluate integrals or moments of functions (such as FE_Q_Hierarchical) – can in general not make sense of the operation that is required for this function. They consequently may not implement it.

◆ memory_consumption()

template<int dim, int spacedim = dim>

virtual std::size_t FiniteElement< dim, spacedim >::memory_consumption ( ) const

virtualinherited

Determine an estimate for the memory consumption (in bytes) of this object.

This function is made virtual, since finite element objects are usually accessed through pointers to their base class, rather than the class itself.

Reimplemented in FE_ABF< dim >, FE_DGVector< PolynomialType, dim, spacedim >, FE_DGVector< PolynomialsBDM< dim >, dim, dim >, FE_DGVector< PolynomialsNedelec< dim >, dim, dim >, FE_DGVector< PolynomialsRaviartThomas< dim >, dim, dim >, FE_DGP< dim, spacedim >, FE_DGPMonomial< dim >, FE_DGPNonparametric< dim, spacedim >, FE_Nedelec< dim >, FE_Poly< dim, spacedim >, FE_Poly< dim, spacedim >, FE_Poly< dim, dim >, FE_Q_Hierarchical< dim >, FE_RaviartThomas< dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ reinit_restriction_and_prolongation_matrices()

template<int dim, int spacedim = dim>

void FiniteElement< dim, spacedim >::reinit_restriction_and_prolongation_matrices	(	const bool	isotropic_restriction_only = `false`,
		const bool	isotropic_prolongation_only = `false`
	)

protectedinherited

Reinit the vectors of restriction and prolongation matrices to the right sizes: For every refinement case, except for RefinementCase::no_refinement, and for every child of that refinement case the space of one restriction and prolongation matrix is allocated, see the documentation of the restriction and prolongation vectors for more detail on the actual vector sizes.

Parameters

isotropic_restriction_only	only the restriction matrices required for isotropic refinement are reinited to the right size.
isotropic_prolongation_only	only the prolongation matrices required for isotropic refinement are reinited to the right size.

◆ interface_constraints_size()

template<int dim, int spacedim = dim>

TableIndices< 2 > FiniteElement< dim, spacedim >::interface_constraints_size ( ) const

protectedinherited

Return the size of interface constraint matrices. Since this is needed in every derived finite element class when initializing their size, it is placed into this function, to avoid having to recompute the dimension- dependent size of these matrices each time.

Note that some elements do not implement the interface constraints for certain polynomial degrees. In this case, this function still returns the size these matrices should have when implemented, but the actual matrices are empty.

◆ compute_n_nonzero_components()

template<int dim, int spacedim = dim>

static std::vector< unsigned int > FiniteElement< dim, spacedim >::compute_n_nonzero_components ( const std::vector< ComponentMask > & nonzero_components )

staticprotectedinherited

Given the pattern of nonzero components for each shape function, compute for each entry how many components are non-zero for each shape function. This function is used in the constructor of this class.

◆ get_face_data() [1/2]

template<int dim, int spacedim = dim>

virtual std::unique_ptr< InternalDataBase > FiniteElement< dim, spacedim >::get_face_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const hp::QCollection< dim - 1 > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedvirtualinherited

Like get_data(), but return an object that will later be used for evaluating shape function information at quadrature points on faces of cells. The object will then be used in calls to implementations of FiniteElement::fill_fe_face_values(). See the documentation of get_data() for more information.

The default implementation of this function converts the face quadrature into a cell quadrature with appropriate quadrature point locations, and with that calls the get_data() function above that has to be implemented in derived classes.

Parameters

[in]	update_flags	A set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_face_values() is called what they are supposed to compute
[in]	mapping	A reference to the mapping used for computing values and derivatives of shape functions.
[in]	quadrature	A reference to the object that describes where the shape functions should be evaluated.
[out]	output_data	A reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_face_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.

Returns: A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Reimplemented in FE_Enriched< dim, spacedim >, FE_PolyFace< PolynomialType, dim, spacedim >, FE_PolyFace< PolynomialSpace< dim - 1 >, dim, dim >, FE_PolyFace< TensorProductPolynomials< dim - 1 >, dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ get_face_data() [2/2]

template<int dim, int spacedim = dim>

virtual std::unique_ptr< InternalDataBase > FiniteElement< dim, spacedim >::get_face_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim - 1 > &	quadrature,
		internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedvirtualinherited

Deprecated:: Use the version taking a hp::QCollection argument.

◆ get_subface_data()

template<int dim, int spacedim = dim>

virtual std::unique_ptr< InternalDataBase > FiniteElement< dim, spacedim >::get_subface_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim - 1 > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedvirtualinherited

Like get_data(), but return an object that will later be used for evaluating shape function information at quadrature points on children of faces of cells. The object will then be used in calls to implementations of FiniteElement::fill_fe_subface_values(). See the documentation of get_data() for more information.

The default implementation of this function converts the face quadrature into a cell quadrature with appropriate quadrature point locations, and with that calls the get_data() function above that has to be implemented in derived classes.

Parameters

[in]	update_flags	A set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_subface_values() is called what they are supposed to compute
[in]	mapping	A reference to the mapping used for computing values and derivatives of shape functions.
[in]	quadrature	A reference to the object that describes where the shape functions should be evaluated.
[out]	output_data	A reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_subface_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.

Returns: A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Reimplemented in FE_Enriched< dim, spacedim >, FE_PolyFace< PolynomialType, dim, spacedim >, FE_PolyFace< PolynomialSpace< dim - 1 >, dim, dim >, FE_PolyFace< TensorProductPolynomials< dim - 1 >, dim, dim >, FESystem< dim, spacedim >, FESystem< dim, dim >, and FESystem< dim, spacedim >.

◆ fill_fe_values() [2/2]

template<int dim, int spacedim = dim>

virtual void FiniteElement< dim, spacedim >::fill_fe_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const CellSimilarity::Similarity	cell_similarity,
		const Quadrature< dim > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedpure virtualinherited

Compute information about the shape functions on the cell denoted by the first argument. Derived classes will have to implement this function based on the kind of element they represent. It is called by FEValues::reinit().

Conceptually, this function evaluates shape functions and their derivatives at the quadrature points represented by the mapped locations of those described by the quadrature argument to this function. In many cases, computing derivatives of shape functions (and in some cases also computing values of shape functions) requires making use of the mapping from the reference to the real cell; this information can either be taken from the mapping_data object that has been filled for the current cell before this function is called, or by calling the member functions of a Mapping object with the mapping_internal object that also corresponds to the current cell.

The information computed by this function is used to fill the various member variables of the output argument of this function. Which of the member variables of that structure should be filled is determined by the update flags stored in the FiniteElement::InternalDataBase::update_each field of the object passed to this function. These flags are typically set by FiniteElement::get_data(), FiniteElement::get_face_date() and FiniteElement::get_subface_data() (or, more specifically, implementations of these functions in derived classes).

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

Parameters

[in]	cell	The cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]	cell_similarity	Whether or not the cell given as first argument is simply a translation, rotation, etc of the cell for which this function was called the most recent time. This information is computed simply by matching the vertices (as stored by the Triangulation) between the previous and the current cell. The value passed here may be modified by implementations of this function and should then be returned (see the discussion of the return value of this function).
[in]	quadrature	A reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the `internal_data` object. The current object is then responsible for evaluating shape functions at the mapped locations of the quadrature points represented by this object.
[in]	mapping	A reference to the mapping object used to map from the reference cell to the current cell. This object was used to compute the information in the `mapping_data` object before the current function was called. It is also the mapping object that created the `mapping_internal` object via Mapping::get_data(). You will need the reference to this mapping object most often to call Mapping::transform() to transform gradients and higher derivatives from the reference to the current cell.
[in]	mapping_internal	An object specific to the mapping object. What the mapping chooses to store in there is of no relevance to the current function, but you may have to pass a reference to this object to certain functions of the Mapping class (e.g., Mapping::transform()) if you need to call them from the current function.
[in]	mapping_data	The output object into which the Mapping::fill_fe_values() function wrote the mapping information corresponding to the current cell. This includes, for example, Jacobians of the mapping that may be of relevance to the current function, as well as other information that FEValues::reinit() requested from the mapping.
[in]	fe_internal	A reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the FiniteElement::InternalDataBase class for an extensive description of the purpose of these objects.
[out]	output_data	A reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the `fe_internal` object.

Note: FEValues ensures that this function is always called with the same pair of fe_internal and output_data objects. In other words, if an implementation of this function knows that it has written a piece of data into the output argument in a previous call, then there is no need to copy it there again in a later call if the implementation knows that this is the same value.

◆ fill_fe_face_values() [2/3]

template<int dim, int spacedim = dim>

virtual void FiniteElement< dim, spacedim >::fill_fe_face_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const hp::QCollection< dim - 1 > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedvirtualinherited

This function is the equivalent to FiniteElement::fill_fe_values(), but for faces of cells. See there for an extensive discussion of its purpose. It is called by FEFaceValues::reinit().

Parameters

[in]	cell	The cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]	face_no	The number of the face we are currently considering, indexed among the faces of the cell specified by the previous argument.
[in]	quadrature	A reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the `internal_data` object. The current object is then responsible for evaluating shape functions at the mapped locations of the quadrature points represented by this object.
[in]	mapping	A reference to the mapping object used to map from the reference cell to the current cell. This object was used to compute the information in the `mapping_data` object before the current function was called. It is also the mapping object that created the `mapping_internal` object via Mapping::get_data(). You will need the reference to this mapping object most often to call Mapping::transform() to transform gradients and higher derivatives from the reference to the current cell.
[in]	mapping_internal	An object specific to the mapping object. What the mapping chooses to store in there is of no relevance to the current function, but you may have to pass a reference to this object to certain functions of the Mapping class (e.g., Mapping::transform()) if you need to call them from the current function.
[in]	mapping_data	The output object into which the Mapping::fill_fe_values() function wrote the mapping information corresponding to the current cell. This includes, for example, Jacobians of the mapping that may be of relevance to the current function, as well as other information that FEValues::reinit() requested from the mapping.
[in]	fe_internal	A reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the FiniteElement::InternalDataBase class for an extensive description of the purpose of these objects.
[out]	output_data	A reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the `fe_internal` object.

◆ fill_fe_face_values() [3/3]

template<int dim, int spacedim = dim>

virtual void FiniteElement< dim, spacedim >::fill_fe_face_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const Quadrature< dim - 1 > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const InternalDataBase &	fe_internal,
		internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedvirtualinherited

Deprecated:: Use the version taking a hp::QCollection argument.

◆ fill_fe_subface_values() [2/2]

template<int dim, int spacedim = dim>

virtual void FiniteElement< dim, spacedim >::fill_fe_subface_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	sub_no,
		const Quadrature< dim - 1 > &	quadrature,
		const Mapping< dim, spacedim > &	mapping,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		const InternalDataBase &	fe_internal,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protectedpure virtualinherited

This function is the equivalent to FiniteElement::fill_fe_values(), but for the children of faces of cells. See there for an extensive discussion of its purpose. It is called by FESubfaceValues::reinit().

Parameters

[in]	cell	The cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]	face_no	The number of the face we are currently considering, indexed among the faces of the cell specified by the previous argument.
[in]	sub_no	The number of the subface, i.e., the number of the child of a face, that we are currently considering, indexed among the children of the face specified by the previous argument.
[in]	quadrature	A reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the `internal_data` object. The current object is then responsible for evaluating shape functions at the mapped locations of the quadrature points represented by this object.
[in]	mapping	A reference to the mapping object used to map from the reference cell to the current cell. This object was used to compute the information in the `mapping_data` object before the current function was called. It is also the mapping object that created the `mapping_internal` object via Mapping::get_data(). You will need the reference to this mapping object most often to call Mapping::transform() to transform gradients and higher derivatives from the reference to the current cell.
[in]	mapping_internal	An object specific to the mapping object. What the mapping chooses to store in there is of no relevance to the current function, but you may have to pass a reference to this object to certain functions of the Mapping class (e.g., Mapping::transform()) if you need to call them from the current function.
[in]	mapping_data	The output object into which the Mapping::fill_fe_values() function wrote the mapping information corresponding to the current cell. This includes, for example, Jacobians of the mapping that may be of relevance to the current function, as well as other information that FEValues::reinit() requested from the mapping.
[in]	fe_internal	A reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the FiniteElement::InternalDataBase class for an extensive description of the purpose of these objects.
[out]	output_data	A reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the `fe_internal` object.

Return the number of degrees per structdim-dimensional object. For structdim==0, the function therefore returns dofs_per_vertex, for structdim==1 dofs_per_line, etc. This function is mostly used to allow some template trickery for functions that should work on all sorts of objects without wanting to use the different names (vertex, line, ...) associated with these objects.

◆ n_components()

template<int dim>

unsigned int FiniteElementData< dim >::n_components ( ) const

inherited

Number of components. See the glossary for more information.

◆ n_blocks()

template<int dim>

unsigned int FiniteElementData< dim >::n_blocks ( ) const

inherited

Number of blocks. See the glossary for more information.

◆ block_indices()

template<int dim>

const BlockIndices & FiniteElementData< dim >::block_indices ( ) const

inherited

Detailed information on block sizes.

◆ tensor_degree()

template<int dim>

unsigned int FiniteElementData< dim >::tensor_degree ( ) const

inherited

Maximal polynomial degree of a shape function in a single coordinate direction.

This function can be used to determine the optimal quadrature rule.

◆ conforms()

template<int dim>

bool FiniteElementData< dim >::conforms ( const Conformity ) const

inherited

Test whether a finite element space conforms to a certain Sobolev space.

Note: This function will return a true value even if the finite element space has higher regularity than asked for.

If true, this element will dominate any other apart from itself in compare_for_domination(). This is because a space that only contains the zero function is definitely smaller (and consequently dominant) when compared to any other finite element space.

Definition at line 351 of file fe_nothing.h.

◆ space_dimension

template<int dim, int spacedim = dim>

constexpr unsigned int FiniteElement< dim, spacedim >::space_dimension = spacedim

staticconstexprinherited

The dimension of the image space, corresponding to Triangulation.

Definition at line 660 of file fe.h.

◆ restriction

template<int dim, int spacedim = dim>

std::vector<std::vector<FullMatrix<double> > > FiniteElement< dim, spacedim >::restriction

protectedinherited

Vector of projection matrices. See get_restriction_matrix() above. The constructor initializes these matrices to zero dimensions, which can be changed by derived classes implementing them.

Note, that restriction[refinement_case-1][child] includes the restriction matrix of child child for the RefinementCase refinement_case. Here, we use refinement_case-1 instead of refinement_case as for RefinementCase::no_refinement(=0) there are no restriction matrices available.

Definition at line 2413 of file fe.h.

◆ prolongation

template<int dim, int spacedim = dim>

std::vector<std::vector<FullMatrix<double> > > FiniteElement< dim, spacedim >::prolongation

protectedinherited

Vector of embedding matrices. See get_prolongation_matrix() above. The constructor initializes these matrices to zero dimensions, which can be changed by derived classes implementing them.

Note, that prolongation[refinement_case-1][child] includes the prolongation matrix of child child for the RefinementCase refinement_case. Here, we use refinement_case-1 instead of refinement_case as for RefinementCase::no_refinement(=0) there are no prolongation matrices available.

Definition at line 2427 of file fe.h.

◆ interface_constraints

template<int dim, int spacedim = dim>

FullMatrix<double> FiniteElement< dim, spacedim >::interface_constraints

protectedinherited

Specify the constraints which the dofs on the two sides of a cell interface underlie if the line connects two cells of which one is refined once.

For further details see the general description of the derived class.

This field is obviously useless in one dimension and has there a zero size.

Definition at line 2439 of file fe.h.

◆ unit_support_points

template<int dim, int spacedim = dim>

std::vector<Point<dim> > FiniteElement< dim, spacedim >::unit_support_points

protectedinherited

List of support points on the unit cell, in case the finite element has any. The constructor leaves this field empty, derived classes may write in some contents.

Finite elements that allow some kind of interpolation operation usually have support points. On the other hand, elements that define their degrees of freedom by, for example, moments on faces, or as derivatives, don't have support points. In that case, this field remains empty.

Definition at line 2451 of file fe.h.

◆ unit_face_support_points

template<int dim, int spacedim = dim>

std::vector<std::vector<Point<dim - 1> > > FiniteElement< dim, spacedim >::unit_face_support_points

protectedinherited

Same for the faces. See the description of the get_unit_face_support_points() function for a discussion of what contributes a face support point.

Definition at line 2458 of file fe.h.

◆ generalized_support_points

template<int dim, int spacedim = dim>

std::vector<Point<dim> > FiniteElement< dim, spacedim >::generalized_support_points

protectedinherited

Support points used for interpolation functions of non-Lagrangian elements.

Definition at line 2464 of file fe.h.

template<int dim, int spacedim = dim>

std::vector<std::pair<unsigned int, unsigned int> > FiniteElement< dim, spacedim >::system_to_component_table

protectedinherited

Store what system_to_component_index() will return.

Definition at line 2507 of file fe.h.

◆ face_system_to_component_table

template<int dim, int spacedim = dim>

std::vector<std::vector<std::pair<unsigned int, unsigned int> > > FiniteElement< dim, spacedim >::face_system_to_component_table

protectedinherited

Map between linear dofs and component dofs on face. This is filled with default values in the constructor, but derived classes will have to overwrite the information if necessary.

By component, we mean the vector component, not the base element. The information thus makes only sense if a shape function is non-zero in only one component.

Definition at line 2519 of file fe.h.

◆ system_to_base_table

template<int dim, int spacedim = dim>

std::vector<std::pair<std::pair<unsigned int, unsigned int>, unsigned int> > FiniteElement< dim, spacedim >::system_to_base_table

protectedinherited

For each shape function, store to which base element and which instance of this base element (in case its multiplicity is greater than one) it belongs, and its index within this base element. If the element is not composed of others, then base and instance are always zero, and the index is equal to the number of the shape function. If the element is composed of single instances of other elements (i.e. all with multiplicity one) all of which are scalar, then base values and dof indices within this element are equal to the system_to_component_table. It differs only in case the element is composed of other elements and at least one of them is vector-valued itself.

This array has valid values also in the case of vector-valued (i.e. non-primitive) shape functions, in contrast to the system_to_component_table.

Definition at line 2538 of file fe.h.

◆ face_system_to_base_table

template<int dim, int spacedim = dim>

std::vector< std::vector<std::pair<std::pair<unsigned int, unsigned int>, unsigned int> > > FiniteElement< dim, spacedim >::face_system_to_base_table

protectedinherited

Likewise for the indices on faces.

Definition at line 2545 of file fe.h.

◆ base_to_block_indices

template<int dim, int spacedim = dim>

BlockIndices FiniteElement< dim, spacedim >::base_to_block_indices

protectedinherited

For each base element, store the number of blocks generated by the base and the first block in a block vector it will generate.

Definition at line 2551 of file fe.h.

◆ component_to_base_table

template<int dim, int spacedim = dim>

std::vector<std::pair<std::pair<unsigned int, unsigned int>, unsigned int> > FiniteElement< dim, spacedim >::component_to_base_table

protectedinherited

The base element establishing a component.

For each component number c, the entries have the following meaning:

table[c].first.first: Number of the base element for c. This is the index you can pass to base_element().
table[c].first.second: Component within the base element for c. This value is between 0 and the n_components() of this base element.
table[c].second: Index of the multiple of the base element that contains c. This value is between 0 and the element_multiplicity() of this base element.

This variable is set to the correct size by the constructor of this class, but needs to be initialized by derived classes, unless its size is one and the only entry is a zero, which is the case for scalar elements. In that case, the initialization by the base class is sufficient.

Note: This table is filled by FETools::Compositing::build_cell_tables().

Definition at line 2574 of file fe.h.

◆ restriction_is_additive_flags

template<int dim, int spacedim = dim>

const std::vector<bool> FiniteElement< dim, spacedim >::restriction_is_additive_flags

protectedinherited

A flag determining whether restriction matrices are to be concatenated or summed up. See the discussion about restriction matrices in the general class documentation for more information.

Definition at line 2581 of file fe.h.

◆ nonzero_components

template<int dim, int spacedim = dim>

template<int dim>

const BlockIndices FiniteElementData< dim >::block_indices_data

inherited

Storage for an object describing the sizes of each block of a compound element. For an element which is not an FESystem, this contains only a single block with length dofs_per_cell.

Definition at line 461 of file fe_data.h.

The documentation for this class was generated from the following files:

include/deal.II/fe/fe_nothing.h
source/fe/fe_nothing.cc

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Attributes

Subscriptor functionality

Support points and interpolation

Detailed Description

FE_Nothing as seen as a function space

FE_Nothing in combination with other elements

FE_Nothing in the context of hanging nodes

Member Enumeration Documentation

◆ Conformity

Constructor & Destructor Documentation

◆ FE_Nothing() [1/2]

◆ FE_Nothing() [2/2]

Member Function Documentation

◆ clone()

◆ get_name()

◆ requires_update_flags()

◆ shape_value()

◆ fill_fe_values() [1/2]

◆ fill_fe_face_values() [1/3]

◆ fill_fe_subface_values() [1/2]

◆ get_data()

◆ compare_for_domination()

◆ hp_vertex_dof_identities()

◆ hp_line_dof_identities()

◆ hp_quad_dof_identities()

◆ hp_constraints_are_implemented()

◆ get_interpolation_matrix()

◆ get_face_interpolation_matrix()

◆ get_subface_interpolation_matrix()

◆ get_constant_modes()

◆ is_dominating()

◆ operator^()

◆ operator[]()

◆ shape_value_component()

◆ shape_grad()

◆ shape_grad_component()

◆ shape_grad_grad()

◆ shape_grad_grad_component()

◆ shape_3rd_derivative()

◆ shape_3rd_derivative_component()

◆ shape_4th_derivative()

◆ shape_4th_derivative_component()

◆ has_support_on_face()

◆ get_restriction_matrix()

◆ get_prolongation_matrix()

◆ prolongation_is_implemented()

◆ isotropic_prolongation_is_implemented()

◆ restriction_is_implemented()

◆ isotropic_restriction_is_implemented()

◆ restriction_is_additive()

◆ constraints()

◆ constraints_are_implemented()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator!=()

◆ system_to_component_index()

◆ component_to_system_index()

◆ face_system_to_component_index()

◆ adjust_quad_dof_index_for_face_orientation()

◆ face_to_cell_index()

◆ adjust_line_dof_index_for_line_orientation()

◆ get_nonzero_components()

◆ n_nonzero_components()

◆ is_primitive() [1/2]

◆ is_primitive() [2/2]

◆ n_base_elements()

◆ base_element()

◆ element_multiplicity()

◆ get_sub_fe() [1/2]

◆ get_sub_fe() [2/2]

◆ system_to_base_index()

◆ face_system_to_base_index()

◆ first_block_of_base()

◆ component_to_base_index()

◆ block_to_base_index()

◆ system_to_block_index()