Reference documentation for deal.II version Git 9c5841c5ee 2019-11-11 14:05:52 -0700
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Public Member Functions | List of all members
FE_Q_iso_Q1< dim, spacedim > Class Template Reference

#include <deal.II/fe/fe_q_iso_q1.h>

Inheritance diagram for FE_Q_iso_Q1< dim, spacedim >:
[legend]

Public Member Functions

 FE_Q_iso_Q1 (const unsigned int n_subdivisions)
 
virtual std::string get_name () const override
 
virtual std::unique_ptr< FiniteElement< dim, spacedim > > clone () 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
 
Functions to support hp
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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
 FE_Q_Base (const TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)
 
virtual void get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override
 
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 bool has_support_on_face (const unsigned int shape_index, const unsigned int face_index) 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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
 FE_Poly (const TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > > &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
 
std::vector< unsigned int > get_poly_space_numbering () const
 
std::vector< unsigned int > get_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
 
- 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 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
 
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 FiniteElementDomination::Domination compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const final
 
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
 
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 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_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
 
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 ()
 
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
 

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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
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 unsigned int dof) 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< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
static std::vector< unsigned int > get_dpo_vector (const unsigned int degree)
 
- 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_Poly< TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > >, dim, spacedim >
TensorProductPolynomials< dim, Polynomials::PiecewisePolynomial< double > > 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< ComponentMasknonzero_components
 
const std::vector< unsigned int > n_nonzero_components_table
 
const bool cached_primitivity
 

Detailed Description

template<int dim, int spacedim = dim>
class FE_Q_iso_Q1< dim, spacedim >

Implementation of a scalar Lagrange finite element Qp-iso-Q1 that defines the finite element space of continuous, piecewise linear elements with p subdivisions in each coordinate direction. It yields an element with the same number of degrees of freedom as the Qp elements but using linear interpolation instead of higher order one. This type of element is also called macro element in the literature as it really consists of several smaller elements, namely pdim such sub-cells.

The numbering of degrees of freedom is done in exactly the same way as in FE_Q of degree p. See there for a detailed description on how degrees of freedom are numbered within one element.

This element represents a Q-linear finite element space on a reduced mesh size h/p. Its effect is equivalent to using FE_Q of degree one on a finer mesh by a factor p if an equivalent quadrature is used. However, this element reduces the flexibility in the choice of (adaptive) mesh size by exactly this factor p, which typically reduces efficiency. On the other hand, comparing this element with p subdivisions to the FE_Q element of degree p on the same mesh shows that the convergence is typically much worse for smooth problems. In particular, Qp elements achieve interpolation orders of hp+1 in the L2 norm, whereas these elements reach only (h/p)2. For these two reasons, this element is usually not very useful as a standalone. In addition, any evaluation of face terms on the boundaries within the elements becomes impossible with this element because deal.II does not have the equivalent of FEFaceValues for lower-dimensional integrals in the interior of cells.

Nonetheless, there are a few use cases where this element actually is useful:

  1. Systems of PDEs where certain variables demand for higher resolutions than the others and the additional degrees of freedom should be spent on increasing the resolution of linears instead of higher order polynomials, and you do not want to use two different meshes for the different components. This can be the case when irregularities (shocks) appear in the solution and stabilization techniques are used that work for linears but not higher order elements.

  2. Stokes/Navier Stokes systems such as the one discussed in step-22 could be solved with Q2-iso-Q1 elements for velocities instead of Q2 elements. Combined with Q1 pressures they give a stable mixed element pair. However, they perform worse than the standard (Taylor-Hood \(Q_2\times Q_1\)) approach in most situations.

  3. Preconditioning systems of FE_Q systems of higher order p with a preconditioner based on Qp-iso-Q1 elements: Some preconditioners like algebraic multigrid perform much better with linear elements than with higher order elements because they often implicitly assume a sparse connectivity between entries. Then, creating a preconditioner matrix based on these elements yields the same number of degrees of freedom (and a spectrally equivalent linear system), which can be combined with a (high order) system matrix in an iterative solver like CG.

Appropriate integration

Due to the nature of these elements as a concatenation of linears, care must be taken when selecting quadrature formulas for this element. The standard choice for an element of p subelements is a formula QIterated<dim>(QGauss<1>(2), p), which corresponds to the formula that would be used for integrating functions on a finer mesh. This is in contrast with FE_Q(p) where QGauss<dim>(p+1) is the default choice. In particular, care must be taken to not use a quadrature formula that evaluates the basis functions (and their derivatives) on sub-element boundaries as the gradients of piecewiese functions on internal boundaries are set to zero. No checks are performed internally to ensure that this is not the case - it is the user's responsibility to avoid these situations.

Also note that the usual deal.II routines for setting up sparsity patterns and assembling matrices do not make use of the increased sparsity in this element compared to FE_Q. This is because DoFTools::make_sparsity_pattern assumes coupling between all degrees of freedom within the element, whereas FE_Q_iso_Q1 with more than one subdivision does have less coupling.

Author
Martin Kronbichler, 2013

Definition at line 113 of file fe_q_iso_q1.h.

Constructor & Destructor Documentation

◆ FE_Q_iso_Q1()

template<int dim, int spacedim>
FE_Q_iso_Q1< dim, spacedim >::FE_Q_iso_Q1 ( const unsigned int  n_subdivisions)

Construct a FE_Q_iso_Q1 element with a given number of subdivisions. The number of subdivision is similar to the degree in FE_Q in the sense that both elements produce the same number of degrees of freedom.

Definition at line 34 of file fe_q_iso_q1.cc.

Member Function Documentation

◆ get_name()

template<int dim, int spacedim>
std::string FE_Q_iso_Q1< dim, spacedim >::get_name ( ) const
overridevirtual

Return a string that uniquely identifies a finite element. This class returns FE_Q_iso_q1<dim>(equivalent_degree), with dim and equivalent_degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 63 of file fe_q_iso_q1.cc.

◆ clone()

template<int dim, int spacedim>
std::unique_ptr< FiniteElement< dim, spacedim > > FE_Q_iso_Q1< 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 101 of file fe_q_iso_q1.cc.

◆ convert_generalized_support_point_values_to_dof_values()

template<int dim, int spacedim>
void FE_Q_iso_Q1< 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

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 80 of file fe_q_iso_q1.cc.

◆ compare_for_domination()

template<int dim, int spacedim>
FiniteElementDomination::Domination FE_Q_iso_Q1< 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 110 of file fe_q_iso_q1.cc.


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