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

Inheritance diagram for FE_Q< dim, spacedim >:

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 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

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

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)

	DeclExceptionMsg (ExcUnitShapeValuesDoNotExist, "You are trying to access the values or derivatives of shape functions " "on the reference cell of an element that does not define its shape " "functions through mapping from the reference cell. Consequently, " "you cannot ask for shape function values or derivatives on the " "reference cell.")

	DeclExceptionMsg (ExcFEHasNoSupportPoints, "You are trying to access the support points of a finite " "element that either has no support points at all, or for " "which the corresponding tables have not been implemented.")

	DeclExceptionMsg (ExcEmbeddingVoid, "You are trying to access the matrices that describe how " "to embed a finite element function on one cell into the " "finite element space on one of its children (i.e., the " "'embedding' or 'prolongation' matrices). However, the " "current finite element can either not define this sort of " "operation, or it has not yet been implemented.")

	DeclExceptionMsg (ExcProjectionVoid, "You are trying to access the matrices that describe how " "to restrict a finite element function from the children " "of one cell to the finite element space defined on their " "parent (i.e., the 'restriction' or 'projection' matrices). " "However, the current finite element can either not define " "this sort of operation, or it has not yet been " "implemented.")

	DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable for the current element " "in the present dimension.")

	DeclException0 (ExcInterpolationNotImplemented)

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 ComponentMask &	get_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 ()

Subscriptor &	operator= (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."<< "\"<< "(Additional information: "<< arg3<< ")\"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")

	DeclException2 (ExcNoSubscriber, char , char ,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")

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

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 >
void	correct_third_derivatives (internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValues::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 InternalDataBase *	get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature, ::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual InternalDataBase *	get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

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

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

Static Protected Member Functions inherited from FE_Q_Base< TensorProductPolynomials< dim >, 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 >, 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< 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

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

1D case:
```
*      0-------1
*   
```

2D case:

*      2-------3
*      |       |
*      |       |
*      |       |
*      0-------1
*

3D case:

*         6-------7        6-------7
*        /|       |       /       /|
*       / |       |      /       / |
*      /  |       |     /       /  |
*     4   |       |    4-------5   |
*     |   2-------3    |       |   3
*     |  /       /     |       |  /
*     | /       /      |       | /
*     |/       /       |       |/
*     0-------1        0-------1
*

The respective coordinate values of the support points of the shape functions are as follows:

Shape function 0: [0, 0, 0];
Shape function 1: [1, 0, 0];
Shape function 2: [0, 1, 0];
Shape function 3: [1, 1, 0];
Shape function 4: [0, 0, 1];
Shape function 5: [1, 0, 1];
Shape function 6: [0, 1, 1];
Shape function 7: [1, 1, 1];

In 2d, these shape functions look as follows:


element, shape function 0	element, shape function 1

element, shape function 2	element, shape function 3

Q2 elements

1D case:
```
*      0---2---1
*   
```

2D case:

*      2---7---3
*      |       |
*      4   8   5
*      |       |
*      0---6---1
*

3D case:
```
*         6--15---7        6--15---7
*        /|       |       /       /|
*      12 |       19     12      1319
*      /  18      |     /       /  |
*     4   |       |    4---14--5   |
*     |   2---11--3    |       |   3
*     |  /       /     |      17  /
*    16 8       9     16       | 9
*     |/       /       |       |/
*     0---10--1        0---10--1
*
*         *-------*        *-------*
*        /|       |       /       /|
*       / |  23   |      /  25   / |
*      /  |       |     /       /  |
*     *   |       |    *-------*   |
*     |20 *-------*    |       |21 *
*     |  /       /     |   22  |  /
*     | /  24   /      |       | /
*     |/       /       |       |/
*     *-------*        *-------*
*   
```
The center vertex has number 26.

The respective coordinate values of the support points of the shape functions are as follows:
- Shape function 0: [0, 0, 0];
- Shape function 1: [1, 0, 0];
- Shape function 2: [0, 1, 0];
- Shape function 3: [1, 1, 0];
- Shape function 4: [0, 0, 1];
- Shape function 5: [1, 0, 1];
- Shape function 6: [0, 1, 1];
- Shape function 7: [1, 1, 1];
- Shape function 8: [0, 1/2, 0];
- Shape function 9: [1, 1/2, 0];
- Shape function 10: [1/2, 0, 0];
- Shape function 11: [1/2, 1, 0];
- Shape function 12: [0, 1/2, 1];
- Shape function 13: [1, 1/2, 1];
- Shape function 14: [1/2, 0, 1];
- Shape function 15: [1/2, 1, 1];
- Shape function 16: [0, 0, 1/2];
- Shape function 17: [1, 0, 1/2];
- Shape function 18: [0, 1, 1/2];
- Shape function 19: [1, 1, 1/2];
- Shape function 20: [0, 1/2, 1/2];
- Shape function 21: [1, 1/2, 1/2];
- Shape function 22: [1/2, 0, 1/2];
- Shape function 23: [1/2, 1, 1/2];
- Shape function 24: [1/2, 1/2, 0];
- Shape function 25: [1/2, 1/2, 1];
- Shape function 26: [1/2, 1/2, 1/2];

In 2d, these shape functions look as follows (the black plane corresponds to zero; negative shape function values may not be visible):


element, shape function 0	element, shape function 1

element, shape function 2	element, shape function 3

element, shape function 4	element, shape function 5

element, shape function 6	element, shape function 7

element, shape function 8

Q3 elements

1D case:
```
*      0--2--3--1
*   
```

2D case:

*      2--10-11-3
*      |        |
*      5  14 15 7
*      |        |
*      4  12 13 6
*      |        |
*      0--8--9--1
*

In 2d, these shape functions look as follows (the black plane corresponds to zero; negative shape function values may not be visible):


element, shape function 0	element, shape function 1

element, shape function 2	element, shape function 3

element, shape function 4	element, shape function 5

element, shape function 6	element, shape function 7

element, shape function 8	element, shape function 9

element, shape function 10	element, shape function 11

element, shape function 12	element, shape function 13

element, shape function 14	element, shape function 15

Q4 elements

1D case:
```
*      0--2--3--4--1
*   
```

2D case:

*      2--13-14-15-3
*      |           |
*      6  22 23 24 9
*      |           |
*      5  19 20 21 8
*      |           |
*      4  16 17 18 7
*      |           |
*      0--10-11-12-1
*

In 2d, these shape functions look as follows (the black plane corresponds to zero; negative shape function values may not be visible):


element, shape function 0	element, shape function 1

element, shape function 2	element, shape function 3

element, shape function 4	element, shape function 5

element, shape function 6	element, shape function 7

element, shape function 8	element, shape function 9

element, shape function 10	element, shape function 11

element, shape function 12	element, shape function 13

element, shape function 14	element, shape function 15

element, shape function 16	element, shape function 17

element, shape function 18	element, shape function 19

element, shape function 20	element, shape function 21

element, shape function 22	element, shape function 23

element, shape function 24

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 522 of file fe_q.h.

Constructor & Destructor Documentation

§ FE_Q() [1/3]

template<int dim, int spacedim>

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

Constructor for tensor product polynomials of degree p.

Definition at line 28 of file fe_q.cc.

§ FE_Q() [2/3]

template<int dim, int spacedim>

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.

Definition at line 52 of file fe_q.cc.

§ FE_Q() [3/3]

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

§ get_name()

template<int dim, int spacedim>

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 >.

Definition at line 74 of file fe_q.cc.

§ clone()

template<int dim, int spacedim>

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 >.

Definition at line 128 of file fe_q.cc.

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

deal.II/fe/fe_q.h
/build/deal.ii-pdtiAo/deal.ii-8.4.2/source/fe/fe_q.cc

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

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

Implementation

Numbering of the degrees of freedom (DoFs)

Q1 elements

Q2 elements

Q3 elements

Q4 elements

Constructor & Destructor Documentation

§ FE_Q() [1/3]

§ FE_Q() [2/3]

§ FE_Q() [3/3]

Member Function Documentation

§ get_name()

§ clone()

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