Reference documentation for deal.II version Git 9deac93 2014-10-24 21:41:49 -0500
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FE_Q< dim, spacedim > Class Template Reference

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

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

Public Member Functions

 FE_Q (const unsigned int p)
 
 FE_Q (const Quadrature< 1 > &points)
 
 FE_Q (const unsigned int subdivisions_per_dimension, const unsigned int base_degree)
 
virtual std::string get_name () const
 
- Public Member Functions inherited from FE_Q_Base< TensorProductPolynomials< dim >, dim, spacedim >
 FE_Q_Base (const TensorProductPolynomials< dim > &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
 
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 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
 
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
 
virtual std::pair< Table
< 2, bool >, std::vector
< unsigned int > > 
get_constant_modes () const
 
virtual bool hp_constraints_are_implemented () const
 
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
FiniteElementDomination::Domination 
compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const
 
- Public Member Functions inherited from FE_Poly< TensorProductPolynomials< dim >, dim, spacedim >
 FE_Poly (const TensorProductPolynomials< 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
 
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
 
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
 
- 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)
 
virtual ~FiniteElement ()
 
const FiniteElement< dim,
spacedim > & 
operator[] (const unsigned int fe_index) const
 
bool operator== (const FiniteElement< dim, spacedim > &) const
 
virtual std::size_t memory_consumption () const
 
 DeclException1 (ExcShapeFunctionNotPrimitive, int,<< "The shape function with index "<< arg1<< " is not primitive, i.e. it is vector-valued and "<< "has more than one non-zero vector component. This "<< "function cannot be called for these shape functions. "<< "Maybe you want to use the same function with the "<< "_component suffix?")
 
 DeclException0 (ExcFENotPrimitive)
 
 DeclException0 (ExcUnitShapeValuesDoNotExist)
 
 DeclException0 (ExcFEHasNoSupportPoints)
 
 DeclException0 (ExcEmbeddingVoid)
 
 DeclException0 (ExcProjectionVoid)
 
 DeclException0 (ExcConstraintsVoid)
 
 DeclException0 (ExcInterpolationNotImplemented)
 
 DeclException0 (ExcBoundaryFaceUsed)
 
 DeclException0 (ExcJacobiDeterminantHasWrongSign)
 
 DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable in the present dimension.")
 
 DeclException2 (ExcComponentIndexInvalid, int, int,<< "The component-index pair ("<< arg1<< ", "<< arg2<< ") is invalid, i.e. non-existent.")
 
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
 
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 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
 
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
 
virtual void interpolate (std::vector< double > &local_dofs, const std::vector< double > &values) const
 
virtual void interpolate (std::vector< double > &local_dofs, const std::vector< Vector< double > > &values, unsigned int offset=0) const
 
virtual void interpolate (std::vector< double > &local_dofs, const VectorSlice< const std::vector< std::vector< double > > > &values) const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
- Public Member Functions inherited from FiniteElementData< dim >
 FiniteElementData ()
 
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const unsigned int n_blocks=numbers::invalid_unsigned_int)
 
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
 
bool is_primitive () const
 
unsigned int tensor_degree () const
 
bool conforms (const Conformity) const
 
bool operator== (const FiniteElementData &) const
 

Protected Member Functions

virtual FiniteElement< dim,
spacedim > * 
clone () const
 
- Protected Member Functions inherited from FE_Q_Base< TensorProductPolynomials< dim >, 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 >, dim, spacedim >
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_data (const UpdateFlags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature) const
 
virtual void fill_fe_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data, CellSimilarity::Similarity &cell_similarity) const
 
virtual void fill_fe_face_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual void fill_fe_subface_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual UpdateFlags update_once (const UpdateFlags flags) const
 
virtual UpdateFlags update_each (const UpdateFlags flags) 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
 
void compute_2nd (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int offset, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_face_data (const UpdateFlags flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature) const
 
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_subface_data (const UpdateFlags flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature) const
 
- Protected Member Functions inherited from FiniteElementData< dim >
void set_primitivity (const bool value)
 

Additional Inherited Members

- Public Types inherited from FiniteElementData< dim >
enum  Conformity {
  unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04,
  H1 = Hcurl | Hdiv, H2 = 0x0e
}
 
- 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
 
BlockIndices block_indices_data
 
- Static Public Attributes inherited from FiniteElement< dim, spacedim >
static const unsigned int space_dimension
 
- Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int dimension = dim
 
- Static Protected Member Functions inherited from FE_Q_Base< TensorProductPolynomials< dim >, dim, spacedim >
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< TensorProductPolynomials< dim >, dim, spacedim >
TensorProductPolynomials< 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
 
- Static Protected Attributes inherited from FiniteElement< dim, spacedim >
static const double fd_step_length
 

Detailed Description

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

Implementation of a scalar Lagrange finite element Qp that yields the finite element space of continuous, piecewise polynomials of degree p in each coordinate direction. 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.

Implementation

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

Furthermore the constructor fills the interface_constraints, the prolongation (embedding) and the restriction matrices. These are implemented only up to a certain degree and may not be available for very high polynomial degree.

Numbering of the degrees of freedom (DoFs)

The original ordering of the shape functions represented by the TensorProductPolynomials 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. To be explicit, these numberings are listed in the following:

Q1 elements

Q2 elements

Q3 elements

Q4 elements

Author
Wolfgang Bangerth, 1998, 2003; Guido Kanschat, 2001; Ralf Hartmann, 2001, 2004, 2005; Oliver Kayser-Herold, 2004; Katharina Kormann, 2008; Martin Kronbichler, 2008

Definition at line 227 of file fe_q.h.

Constructor & Destructor Documentation

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

Constructor for tensor product polynomials of degree p.

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

Constructor for tensor product polynomials with support points points 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. If FE_Q<dim>(QGaussLobatto<1>(fe_degree+1)) is specified, so-called Gauss-Lobatto elements are obtained which can give a diagonal mass matrix if combined with Gauss-Lobatto quadrature on the same points. Their use is shown in step-48.

template<int dim, int spacedim = dim>
FE_Q< dim, spacedim >::FE_Q ( const unsigned int  subdivisions_per_dimension,
const unsigned int  base_degree 
)

Constructs a FE_Q_isoQ1 element. That element shares large parts of code with FE_Q so most of the construction work is done in this routine, whereas the public constructor is in the class FE_Q_isoQ1.

Member Function Documentation

template<int dim, int spacedim = dim>
virtual std::string FE_Q< dim, spacedim >::get_name ( ) const
virtual

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

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual FiniteElement<dim,spacedim>* FE_Q< dim, spacedim >::clone ( ) const
protectedvirtual

clone function instead of a copy constructor.

This function is needed by the constructors of FESystem.

Implements FiniteElement< dim, spacedim >.


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