Reference documentation for deal.II version 9.2.0
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Public Member Functions | Static Private Member Functions | List of all members
FE_Q_DG0< dim, spacedim > Class Template Reference

#include <deal.II/fe/fe_q_dg0.h>

Inheritance diagram for FE_Q_DG0< dim, spacedim >:
[legend]

Public Member Functions

 FE_Q_DG0 (const unsigned int p)
 
 FE_Q_DG0 (const Quadrature< 1 > &points)
 
virtual std::string get_name () const override
 
virtual void convert_generalized_support_point_values_to_dof_values (const std::vector< Vector< double >> &support_point_values, std::vector< double > &nodal_values) const override
 
virtual void get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override
 
virtual bool has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const override
 
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes () const override
 
virtual std::unique_ptr< FiniteElement< dim, spacedim > > clone () const override
 
virtual FiniteElementDomination::Domination compare_for_domination (const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const override final
 
- Public Member Functions inherited from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >
 FE_Q_Base (const TensorProductPolynomialsConst< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)
 
virtual void get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override
 
virtual void get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix) const override
 
virtual const FullMatrix< double > & get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override
 
virtual const FullMatrix< double > & get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override
 
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 override
 
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes () const override
 
virtual bool hp_constraints_are_implemented () const override
 
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 override
 
- Public Member Functions inherited from FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
 FE_Poly (const TensorProductPolynomialsConst< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)
 
unsigned int get_degree () const
 
virtual UpdateFlags requires_update_flags (const UpdateFlags update_flags) const override
 
std::vector< unsigned intget_poly_space_numbering () const
 
std::vector< unsigned intget_poly_space_numbering_inverse () const
 
virtual double shape_value (const unsigned int i, const Point< dim > &p) const override
 
virtual double shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 1, dim > shape_grad (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 1, dim > shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 2, dim > shape_grad_grad (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 2, dim > shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 3, dim > shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 3, dim > shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 4, dim > shape_4th_derivative (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 4, dim > shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual std::size_t memory_consumption () const override
 
- 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 () override=default
 
std::pair< std::unique_ptr< FiniteElement< dim, spacedim > >, unsigned intoperator^ (const unsigned int multiplicity) const
 
const FiniteElement< dim, spacedim > & operator[] (const unsigned int fe_index) 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 bool hp_constraints_are_implemented () const
 
virtual FiniteElementDomination::Domination compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const final
 
virtual bool operator== (const FiniteElement< dim, spacedim > &fe) const
 
bool operator!= (const FiniteElement< dim, spacedim > &) const
 
std::pair< unsigned int, unsigned intsystem_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 intface_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
 
unsigned int adjust_line_dof_index_for_line_orientation (const unsigned int index, const bool line_orientation) const
 
const ComponentMaskget_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 intsystem_to_base_index (const unsigned int index) const
 
std::pair< std::pair< unsigned int, unsigned int >, unsigned intface_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 intcomponent_to_base_index (const unsigned int component) const
 
std::pair< unsigned int, unsigned intblock_to_base_index (const unsigned int block) const
 
std::pair< unsigned int, types::global_dof_indexsystem_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
 
GeometryPrimitive get_associated_geometry_primitive (const unsigned int cell_dof_index) const
 
virtual std::size_t memory_consumption () const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&) noexcept
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&) noexcept
 
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)
 
- 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 BlockIndicesblock_indices () const
 
unsigned int tensor_degree () const
 
bool conforms (const Conformity) const
 
bool operator== (const FiniteElementData &) const
 

Static Private Member Functions

static std::vector< boolget_riaf_vector (const unsigned int degree)
 
static std::vector< unsigned intget_dpo_vector (const unsigned int degree)
 

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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >
static ::ExceptionBaseExcFEQCannotHaveDegree0 ()
 
- Static Public Member Functions inherited from FiniteElement< dim, spacedim >
static ::ExceptionBaseExcShapeFunctionNotPrimitive (int arg1)
 
static ::ExceptionBaseExcFENotPrimitive ()
 
static ::ExceptionBaseExcUnitShapeValuesDoNotExist ()
 
static ::ExceptionBaseExcFEHasNoSupportPoints ()
 
static ::ExceptionBaseExcEmbeddingVoid ()
 
static ::ExceptionBaseExcProjectionVoid ()
 
static ::ExceptionBaseExcWrongInterfaceMatrixSize (int arg1, int arg2)
 
static ::ExceptionBaseExcInterpolationNotImplemented ()
 
- Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >
void initialize (const std::vector< Point< 1 >> &support_points_1d)
 
void initialize_constraints (const std::vector< Point< 1 >> &points)
 
void initialize_unit_support_points (const std::vector< Point< 1 >> &points)
 
void initialize_unit_face_support_points (const std::vector< Point< 1 >> &points)
 
void initialize_quad_dof_index_permutation ()
 
- Protected Member Functions inherited from FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBaseget_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &, const Quadrature< dim > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) 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
 
void fill_fe_values (const Triangulation< 1, 2 >::cell_iterator &, const CellSimilarity::Similarity cell_similarity, const Quadrature< 1 > &quadrature, const Mapping< 1, 2 > &mapping, const Mapping< 1, 2 >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< 1, 2 > &mapping_data, const FiniteElement< 1, 2 >::InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< 1, 2 > &output_data) const
 
void fill_fe_values (const Triangulation< 2, 3 >::cell_iterator &, const CellSimilarity::Similarity cell_similarity, const Quadrature< 2 > &quadrature, const Mapping< 2, 3 > &mapping, const Mapping< 2, 3 >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< 2, 3 > &mapping_data, const FiniteElement< 2, 3 >::InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< 2, 3 > &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 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
 
void correct_hessians (internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const unsigned int n_q_points) const
 
void correct_third_derivatives (internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const unsigned int n_q_points) const
 
- 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 std::unique_ptr< InternalDataBaseget_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< InternalDataBaseget_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 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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >
static std::vector< unsigned intget_dpo_vector (const unsigned int degree)
 
- Static Protected Member Functions inherited from FiniteElement< dim, spacedim >
static std::vector< unsigned intcompute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)
 
- Protected Attributes inherited from FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
TensorProductPolynomialsConst< dim > poly_space
 
- Protected Attributes inherited from FiniteElement< dim, spacedim >
std::vector< std::vector< FullMatrix< double > > > restriction
 
std::vector< std::vector< FullMatrix< double > > > prolongation
 
FullMatrix< doubleinterface_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, intadjust_quad_dof_index_for_face_orientation_table
 
std::vector< intadjust_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< boolrestriction_is_additive_flags
 
const std::vector< ComponentMasknonzero_components
 
const std::vector< unsigned intn_nonzero_components_table
 
const bool cached_primitivity
 

Detailed Description

template<int dim, int spacedim = dim>
class FE_Q_DG0< dim, spacedim >

Implementation of a scalar Lagrange finite element Qp+DG0 that yields the finite element space of continuous, piecewise polynomials of degree p in each coordinate direction plus the space of locally constant functions. This class is realized using tensor product polynomials based on equidistant or given support points.

The standard constructor of this class takes the degree p of this finite element. Alternatively, it can take a quadrature formula points defining the support points of the Lagrange interpolation in one coordinate direction.

For more information about the spacedim template parameter check the documentation of FiniteElement or the one of Triangulation.

For more information regarding this element see: Boffi, D., et al. "Local Mass Conservation of Stokes Finite Elements." Journal of Scientific Computing (2012): 1-18.

Implementation

The constructor creates a TensorProductPolynomials object that includes the tensor product of LagrangeEquidistant polynomials of degree p plus the locally constant function. This TensorProductPolynomialsConst object provides all values and derivatives of the shape functions. In case a quadrature rule is given, the constructor creates a TensorProductPolynomialsConst object that includes the tensor product of Lagrange polynomials with the support points from points and a locally constant function.

Furthermore the constructor fills the interface_constrains, the prolongation (embedding) and the restriction matrices.

Numbering of the degrees of freedom (DoFs)

The original ordering of the shape functions represented by the TensorProductPolynomialsConst is a tensor product numbering. However, the shape functions on a cell are renumbered beginning with the shape functions whose support points are at the vertices, then on the line, on the quads, and finally (for 3d) on the hexes. Finally there is a support point for the discontinuous shape function in the middle of the cell. To be explicit, these numberings are listed in the following:

Q1 elements

Q2 elements

Q3 elements

Q4 elements

Definition at line 239 of file fe_q_dg0.h.

Constructor & Destructor Documentation

◆ FE_Q_DG0() [1/2]

template<int dim, int spacedim>
FE_Q_DG0< dim, spacedim >::FE_Q_DG0 ( const unsigned int  p)

Constructor for tensor product polynomials of degree p plus locally constant functions.

Definition at line 36 of file fe_q_dg0.cc.

◆ FE_Q_DG0() [2/2]

template<int dim, int spacedim>
FE_Q_DG0< dim, spacedim >::FE_Q_DG0 ( const Quadrature< 1 > &  points)

Constructor for tensor product polynomials with support points points plus locally constant functions based on a one-dimensional quadrature formula. The degree of the finite element is points.size()-1. Note that the first point has to be 0 and the last one 1.

Definition at line 64 of file fe_q_dg0.cc.

Member Function Documentation

◆ get_name()

template<int dim, int spacedim>
std::string FE_Q_DG0< dim, spacedim >::get_name
overridevirtual

Return a string that uniquely identifies a finite element. This class returns FE_Q_DG0<dim>(degree), with dim and degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 95 of file fe_q_dg0.cc.

◆ convert_generalized_support_point_values_to_dof_values()

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::convert_generalized_support_point_values_to_dof_values ( const std::vector< Vector< double >> &  support_point_values,
std::vector< double > &  nodal_values 
) const
overridevirtual

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_valuesAn 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_valuesAn 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.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 183 of file fe_q_dg0.cc.

◆ get_interpolation_matrix()

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::get_interpolation_matrix ( const FiniteElement< dim, spacedim > &  source,
FullMatrix< double > &  matrix 
) const
overridevirtual

Return the matrix interpolating from the given finite element to the present one. The size of the matrix is then dofs_per_cell times source.dofs_per_cell.

These matrices are only available if the source element is also a FE_Q_DG0 element. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >.

Definition at line 211 of file fe_q_dg0.cc.

◆ has_support_on_face()

template<int dim, int spacedim>
bool FE_Q_DG0< dim, spacedim >::has_support_on_face ( const unsigned int  shape_index,
const unsigned int  face_index 
) const
overridevirtual

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

Reimplemented from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, dim >.

Definition at line 262 of file fe_q_dg0.cc.

◆ get_constant_modes()

template<int dim, int spacedim>
std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_Q_DG0< dim, spacedim >::get_constant_modes
overridevirtual

Return a list of constant modes of the element. For this element, there are two constant modes despite the element is scalar: The first constant mode is all ones for the usual FE_Q basis and the second one only using the discontinuous part.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 278 of file fe_q_dg0.cc.

◆ clone()

template<int dim, int spacedim>
std::unique_ptr< FiniteElement< dim, spacedim > > FE_Q_DG0< 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 174 of file fe_q_dg0.cc.

◆ compare_for_domination()

template<int dim, int spacedim>
FiniteElementDomination::Domination FE_Q_DG0< 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.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 297 of file fe_q_dg0.cc.

◆ get_riaf_vector()

template<int dim, int spacedim>
std::vector< bool > FE_Q_DG0< dim, spacedim >::get_riaf_vector ( const unsigned int  degree)
staticprivate

Return the restriction_is_additive flags. Only the last component is true.

Definition at line 237 of file fe_q_dg0.cc.

◆ get_dpo_vector()

template<int dim, int spacedim>
std::vector< unsigned int > FE_Q_DG0< dim, spacedim >::get_dpo_vector ( const unsigned int  degree)
staticprivate

Only for internal use. Its full name is get_dofs_per_object_vector function and it creates the dofs_per_object vector that is needed within the constructor to be passed to the constructor of FiniteElementData.

Definition at line 248 of file fe_q_dg0.cc.


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