Cubic Lagrangian finite elment on a triangular reference element. More...

#include <lf/uscalfe/uscalfe.h>

Inheritance diagram for lf::uscalfe::FeLagrangeO3Tria< SCALAR >:

Public Member Functions
	FeLagrangeO3Tria (const FeLagrangeO3Tria &)=default

	FeLagrangeO3Tria (FeLagrangeO3Tria &&) noexcept=default

FeLagrangeO3Tria &	operator= (const FeLagrangeO3Tria &)=default

FeLagrangeO3Tria &	operator= (FeLagrangeO3Tria &&) noexcept=default

	FeLagrangeO3Tria ()=default

	~FeLagrangeO3Tria () override=default

base::RefEl	RefEl () const override
	Tells the type of reference cell underlying the parametric finite element.

unsigned	Degree () const override
	Quadratic Lagrangian finite elements rely on polynomials of degree 3.

size_type	NumRefShapeFunctions () const override
	Ten local shape functions are associated with a triangular cell in the case of cubic Lagrangian finite elements.

size_type	NumRefShapeFunctions (dim_t codim) const override
	One shape function attached to each node and two to each edge of the triangle. There is one interior shape function.

size_type	NumRefShapeFunctions (dim_t codim, sub_idx_t subidx) const override
	One shape function attached to each node and two to each edge of the triangle. There is one interior shape function.

Eigen::Matrix< SCALAR, Eigen::Dynamic, Eigen::Dynamic >	EvalReferenceShapeFunctions (const Eigen::MatrixXd &refcoords) const override
	Point evaluation of reference shape functions.

Eigen::Matrix< SCALAR, Eigen::Dynamic, Eigen::Dynamic >	GradientsReferenceShapeFunctions (const Eigen::MatrixXd &refcoords) const override
	Point evaluations of gradients of reference shape functions.

Eigen::MatrixXd	EvaluationNodes () const override
	Evaluation nodes are the three vertices of the triangle, two equispaced interio nodes for each edge, a the barycentre.

size_type	NumEvaluationNodes () const override
	Ten evaluation nodes.

Public Member Functions inherited from lf::fe::ScalarReferenceFiniteElement< SCALAR >
virtual	~ScalarReferenceFiniteElement ()=default

dim_t	Dimension () const
	Returns the spatial dimension of the reference cell.

virtual Eigen::Matrix< SCALAR, 1, Eigen::Dynamic >	NodalValuesToDofs (const Eigen::Matrix< SCALAR, 1, Eigen::Dynamic > &nodvals) const
	Computes the linear combination of reference shape functions matching function values at evaluation nodes.

Additional Inherited Members
Public Types inherited from lf::fe::ScalarReferenceFiniteElement< SCALAR >
using	Scalar = SCALAR
	The underlying scalar type.

Protected Member Functions inherited from lf::fe::ScalarReferenceFiniteElement< SCALAR >
	ScalarReferenceFiniteElement ()=default

	ScalarReferenceFiniteElement (const ScalarReferenceFiniteElement &)=default

	ScalarReferenceFiniteElement (ScalarReferenceFiniteElement &&) noexcept=default

ScalarReferenceFiniteElement &	operator= (const ScalarReferenceFiniteElement &)=default

ScalarReferenceFiniteElement &	operator= (ScalarReferenceFiniteElement &&) noexcept=default

Related Symbols inherited from lf::fe::ScalarReferenceFiniteElement< SCALAR >
template<class SCALAR >
void	PrintInfo (std::ostream &o, const ScalarReferenceFiniteElement< SCALAR > &srfe, unsigned int ctrl=0)
	Print information about a ScalarReferenceFiniteElement to the given stream.

template<typename SCALAR >
std::ostream &	operator<< (std::ostream &o, const ScalarReferenceFiniteElement< SCALAR > &fe_desc)
	Stream output operator: just calls the ScalarReferenceFiniteElement::print() method.

Detailed Description

template<typename SCALAR>
class lf::uscalfe::FeLagrangeO3Tria< SCALAR >

Cubic Lagrangian finite elment on a triangular reference element.

This is a specialization of ScalarReferenceFiniteElement. Refer to its documentation.

The 10 reference shape functions are combinations of the barycentric coordinate functions on the reference triangle.

The first three shape functions are associated with vertices, the next six with edges of the triangle. The last shape function is an interior shape function, see Example 2.6.1.7 for the location of interpolation nodes.

See also: ScalarReferenceFiniteElement

Definition at line 945 of file lagr_fe.h.

Constructor & Destructor Documentation

◆ FeLagrangeO3Tria() [1/3]

template<typename SCALAR >

lf::uscalfe::FeLagrangeO3Tria< SCALAR >::FeLagrangeO3Tria ( const FeLagrangeO3Tria< SCALAR > & )

default

◆ FeLagrangeO3Tria() [2/3]

template<typename SCALAR >

lf::uscalfe::FeLagrangeO3Tria< SCALAR >::FeLagrangeO3Tria ( FeLagrangeO3Tria< SCALAR > && )

defaultnoexcept

◆ FeLagrangeO3Tria() [3/3]

template<typename SCALAR >

lf::uscalfe::FeLagrangeO3Tria< SCALAR >::FeLagrangeO3Tria ( )

default

◆ ~FeLagrangeO3Tria()

template<typename SCALAR >

lf::uscalfe::FeLagrangeO3Tria< SCALAR >::~FeLagrangeO3Tria ( )

overridedefault

Member Function Documentation

◆ Degree()

template<typename SCALAR >

unsigned lf::uscalfe::FeLagrangeO3Tria< SCALAR >::Degree ( ) const

inlineoverridevirtual

Quadratic Lagrangian finite elements rely on polynomials of degree 3.

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 962 of file lagr_fe.h.

◆ EvalReferenceShapeFunctions()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, Eigen::Dynamic > lf::uscalfe::FeLagrangeO3Tria< SCALAR >::EvalReferenceShapeFunctions ( const Eigen::MatrixXd & refcoords ) const

inlineoverridevirtual

Point evaluation of reference shape functions.

The reference shape function are cardinal basis functions of the space of cubic polynomials with respect to the ten interpolation nodes supplied by the lattive drawn in Figure 111.

See also: fe::ScalarReferenceFiniteElement::EvalReferenceShapeFunctions()

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 1010 of file lagr_fe.h.

◆ EvaluationNodes()

template<typename SCALAR >

Eigen::MatrixXd lf::uscalfe::FeLagrangeO3Tria< SCALAR >::EvaluationNodes ( ) const

inlineoverridevirtual

Evaluation nodes are the three vertices of the triangle, two equispaced interio nodes for each edge, a the barycentre.

The reference shape functions as implemented by this class are a cardinal basis of the space of cubic two-variate polynomials with respect to these evaluation nodes.

The numbering of evluation nodes is fixed by the numbering of the local shape functions.

See also: fe::ScalarReferenceFiniteElement::EvaluationNodes()

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 1115 of file lagr_fe.h.

◆ GradientsReferenceShapeFunctions()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, Eigen::Dynamic > lf::uscalfe::FeLagrangeO3Tria< SCALAR >::GradientsReferenceShapeFunctions ( const Eigen::MatrixXd & refcoords ) const

inlineoverridevirtual

Point evaluations of gradients of reference shape functions.

Compute values of gradients of reference shape functions at specified nodes

See also: fe::ScalarReferenceFiniteElement::GradientsReferenceShapeFunctions()

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 1053 of file lagr_fe.h.

◆ NumEvaluationNodes()

template<typename SCALAR >

size_type lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumEvaluationNodes ( ) const

inlineoverridevirtual

Ten evaluation nodes.

Tell the number of evaluation (interpolation) nodes.

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 1137 of file lagr_fe.h.

References lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumRefShapeFunctions().

◆ NumRefShapeFunctions() [1/3]

template<typename SCALAR >

size_type lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumRefShapeFunctions ( ) const

inlineoverridevirtual

Ten local shape functions are associated with a triangular cell in the case of cubic Lagrangian finite elements.

See also: fe::ScalarReferenceFiniteElement::NumRefShapeFunctions()

Reimplemented from lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 969 of file lagr_fe.h.

Referenced by lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumEvaluationNodes().

◆ NumRefShapeFunctions() [2/3]

template<typename SCALAR >

size_type lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumRefShapeFunctions ( dim_t codim ) const

inlineoverridevirtual

One shape function attached to each node and two to each edge of the triangle. There is one interior shape function.

The number of interior reference shape functions for sub-entities of a particular co-dimension.

Parameters

codim co-dimension of the subentity

Returns: number of interior reference shape function belonging to the specified sub-entity.

Note: this method will throw an exception when different numbers of reference shape functions are assigned to different sub-entities of the same co-dimension

Reimplemented from lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 979 of file lagr_fe.h.

◆ NumRefShapeFunctions() [3/3]

template<typename SCALAR >

size_type lf::uscalfe::FeLagrangeO3Tria< SCALAR >::NumRefShapeFunctions	(	dim_t	codim,
		sub_idx_t	subidx ) const

inlineoverridevirtual

One shape function attached to each node and two to each edge of the triangle. There is one interior shape function.

The number of interior reference shape functions for every sub-entity.

Parameters

codim	do-dimension of the subentity
subidx	local index of the sub-entity

Returns: number of interior reference shape function belonging to the specified sub-entity.

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 992 of file lagr_fe.h.

◆ operator=() [1/2]

template<typename SCALAR >

FeLagrangeO3Tria & lf::uscalfe::FeLagrangeO3Tria< SCALAR >::operator= ( const FeLagrangeO3Tria< SCALAR > & )

default

◆ operator=() [2/2]

template<typename SCALAR >

FeLagrangeO3Tria & lf::uscalfe::FeLagrangeO3Tria< SCALAR >::operator= ( FeLagrangeO3Tria< SCALAR > && )

defaultnoexcept

◆ RefEl()

template<typename SCALAR >

base::RefEl lf::uscalfe::FeLagrangeO3Tria< SCALAR >::RefEl ( ) const

inlineoverridevirtual

Tells the type of reference cell underlying the parametric finite element.

Implements lf::fe::ScalarReferenceFiniteElement< SCALAR >.

Definition at line 955 of file lagr_fe.h.

References lf::base::RefEl::kTria().

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

/__w/lehrfempp/lehrfempp/lib/lf/uscalfe/lagr_fe.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ FeLagrangeO3Tria() [1/3]

◆ FeLagrangeO3Tria() [2/3]

◆ FeLagrangeO3Tria() [3/3]

◆ ~FeLagrangeO3Tria()

Member Function Documentation

◆ Degree()

◆ EvalReferenceShapeFunctions()

◆ EvaluationNodes()

◆ GradientsReferenceShapeFunctions()

◆ NumEvaluationNodes()

◆ NumRefShapeFunctions() [1/3]

◆ NumRefShapeFunctions() [2/3]

◆ NumRefShapeFunctions() [3/3]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ RefEl()