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

Inheritance diagram for FE_FaceQ< dim, spacedim >:

Public Member Functions
	FE_FaceQ (const unsigned int p)

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

virtual std::string	get_name () 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 void	get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const

virtual void	get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix) const

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

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

Functions to support hp
virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_vertex_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const

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

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

virtual bool	hp_constraints_are_implemented () const

virtual FiniteElementDomination::Domination	compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const

Public Member Functions inherited from FE_PolyFace< TensorProductPolynomials< dim-1 >, dim, spacedim >
	FE_PolyFace (const TensorProductPolynomials< dim-1 > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)

unsigned int	get_degree () const

Public Member Functions inherited from FiniteElement< dim, spacedim >
	FiniteElement (const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)

	FiniteElement (FiniteElement< dim, spacedim > &&)=default

	FiniteElement (const FiniteElement< dim, spacedim > &)=default

virtual	~FiniteElement ()=default

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

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

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

virtual std::size_t	memory_consumption () const

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

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 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

virtual void	get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const

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	adjust_quad_dof_index_for_face_orientation (const unsigned int index, 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

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

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

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

bool	has_face_support_points () const

virtual Point< dim-1 >	unit_face_support_point (const unsigned int index) const

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

bool	has_generalized_support_points () const

const std::vector< Point< dim-1 > > &	get_generalized_face_support_points () const

bool	has_generalized_face_support_points () const

GeometryPrimitive	get_associated_geometry_primitive (const unsigned int cell_dof_index) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

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

Public Member Functions inherited from FiniteElementData< dim >
	FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())

unsigned int	n_dofs_per_vertex () const

unsigned int	n_dofs_per_line () const

unsigned int	n_dofs_per_quad () const

unsigned int	n_dofs_per_hex () const

unsigned int	n_dofs_per_face () const

unsigned int	n_dofs_per_cell () const

template<int structdim>
unsigned int	n_dofs_per_object () 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

bool	operator== (const FiniteElementData &) const

Static Private Member Functions
static std::vector< unsigned int >	get_dpo_vector (const unsigned int deg)

Additional Inherited Members
Public Types inherited from FiniteElementData< dim >
enum	Conformity { unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04, H1 = Hcurl \| Hdiv, H2 = 0x0e }

Static Public Member Functions inherited from FiniteElement< dim, spacedim >
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 ()

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Public Attributes inherited from FiniteElementData< dim >
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 inherited from FiniteElement< dim, spacedim >
static const unsigned int	space_dimension = spacedim

Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int	dimension = dim

Protected Member Functions inherited from FiniteElement< dim, spacedim >
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 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 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

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 Protected Member Functions inherited from FiniteElement< dim, spacedim >
static std::vector< unsigned int >	compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)

Protected Attributes inherited from FE_PolyFace< TensorProductPolynomials< dim-1 >, dim, spacedim >
TensorProductPolynomials< dim-1 >	poly_space

Protected Attributes inherited from FiniteElement< dim, spacedim >
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< Point< dim-1 > >	unit_face_support_points

std::vector< Point< dim > >	generalized_support_points

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

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::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::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

Detailed Description

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

A finite element that is a tensor product polynomial on each face and undefined in the interior of the cells. The basis functions on the faces are Lagrange polynomials based on the support points of the (dim-1)-dimensional Gauss–Lobatto quadrature rule. For element degree one and two, the polynomials hence correspond to the usual Lagrange polynomials on equidistant points.

Although the name does not give it away, the element is discontinuous at locations where faces of cells meet. In particular, this finite element is the trace space of FE_RaviartThomas on the faces and serves in hybridized methods, e.g. in combination with the FE_DGQ element. Its use is demonstrated in the step-51 tutorial program.

Note: Since this element is defined only on faces, only FEFaceValues and FESubfaceValues will provide useful information. On the other hand, if you use this element with FEValues for cell integration, then the values and derivatives of shape functions will have invalid values and will not likely produce anything useful. In order to make the use of this element as part of an FESystem simpler, using a (cell) FEValues object will not fail outright, but those components of shape functions of the combined element that correspond to FE_FaceQ will have the invalid values mentioned above.

Author: Guido Kanschat, Martin Kronbichler

Date: 2009, 2011, 2013

Definition at line 55 of file fe_face.h.

Constructor & Destructor Documentation

◆ FE_FaceQ()

template<int dim, int spacedim>

FE_FaceQ< dim, spacedim >::FE_FaceQ ( const unsigned int p )

Constructor for tensor product polynomials of degree p. The shape functions created using this constructor correspond to Lagrange polynomials in each coordinate direction.

Definition at line 49 of file fe_face.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

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

virtual

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 114 of file fe_face.cc.

◆ get_name()

template<int dim, int spacedim>

std::string FE_FaceQ< dim, spacedim >::get_name ( ) const

virtual

Return a string that uniquely identifies a finite element. This class returns FE_FaceQ<dim>(degree), with dim and degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 123 of file fe_face.cc.

◆ convert_generalized_support_point_values_to_dof_values()

template<int dim, int spacedim>

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

virtual

Implementation of the corresponding function in the FiniteElement class. Since the current element is interpolatory, the nodal values are exactly the support point values. Furthermore, since the current element is scalar, the support point values need to be vectors of length 1.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 477 of file fe_face.cc.

◆ get_face_interpolation_matrix()

template<int dim, int spacedim>

void FE_FaceQ< dim, spacedim >::get_face_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		FullMatrix< double > &	matrix
	)		const

virtual

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. This element only provides interpolation matrices for elements of the same type and FE_Nothing. For all other elements, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 141 of file fe_face.cc.

◆ get_subface_interpolation_matrix()

template<int dim, int spacedim>

void FE_FaceQ< dim, spacedim >::get_subface_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		const unsigned int	subface,
		FullMatrix< double > &	matrix
	)		const

virtual

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. This element only provides interpolation matrices for elements of the same type and FE_Nothing. For all other elements, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 153 of file fe_face.cc.

◆ has_support_on_face()

template<int dim, int spacedim>

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

virtual

This function returns true, if the shape function shape_index has non-zero function values somewhere on the face face_index.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 241 of file fe_face.cc.

◆ hp_vertex_dof_identities()

template<int dim, int spacedim>

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

virtual

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 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.

The set of such constraints is non-empty only for dim==1.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 275 of file fe_face.cc.

◆ hp_line_dof_identities()

template<int dim, int spacedim>

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

virtual

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

The set of such constraints is non-empty only for dim==2.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 287 of file fe_face.cc.

◆ hp_quad_dof_identities()

template<int dim, int spacedim>

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

virtual

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

The set of such constraints is non-empty only for dim==3.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 356 of file fe_face.cc.

◆ hp_constraints_are_implemented()

template<int dim, int spacedim>

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

virtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible".

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 265 of file fe_face.cc.

◆ compare_for_face_domination()

template<int dim, int spacedim>

FiniteElementDomination::Domination FE_FaceQ< dim, spacedim >::compare_for_face_domination ( const FiniteElement< dim, spacedim > & fe_other ) const

virtual

Return whether this element dominates the one given as argument when they meet at a common face, whether it is the other way around, whether neither dominates, or if either could dominate.

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

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 431 of file fe_face.cc.

◆ get_constant_modes()

template<int dim, int spacedim>

std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_FaceQ< dim, spacedim >::get_constant_modes ( ) const

virtual

Return a list of constant modes of the element. For this element, it simply returns one row with all entries set to true.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 465 of file fe_face.cc.

◆ get_dpo_vector()

template<int dim, int spacedim>

std::vector< unsigned int > FE_FaceQ< dim, spacedim >::get_dpo_vector ( const unsigned int deg )

staticprivate

Return vector with dofs per vertex, line, quad, hex.

Definition at line 252 of file fe_face.cc.

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

deal.II/fe/fe_face.h
source/fe/fe_face.cc

Public Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ FE_FaceQ()

Member Function Documentation

◆ clone()

◆ get_name()

◆ convert_generalized_support_point_values_to_dof_values()

◆ get_face_interpolation_matrix()

◆ get_subface_interpolation_matrix()

◆ has_support_on_face()

◆ hp_vertex_dof_identities()

◆ hp_line_dof_identities()

◆ hp_quad_dof_identities()

◆ hp_constraints_are_implemented()

◆ compare_for_face_domination()

◆ get_constant_modes()

◆ get_dpo_vector()

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