Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k > Class Template Reference

Nédélec elements of the first kind for simplex elements. More...

#include <dune/localfunctions/nedelec/nedelec1stkindsimplex.hh>

Public Types
using	Traits = LocalFiniteElementTraits< Impl::Nedelec1stKindSimplexLocalBasis< D, R, dim, k >, Impl::Nedelec1stKindSimplexLocalCoefficients< dim, k >, Impl::Nedelec1stKindSimplexLocalInterpolation< Impl::Nedelec1stKindSimplexLocalBasis< D, R, dim, k > > >

Public Member Functions
	Nedelec1stKindSimplexLocalFiniteElement ()=default
	Default constructor.
	Nedelec1stKindSimplexLocalFiniteElement (std::bitset< dim *(dim+1)/2 > s)
	Constructor with explicitly given edge orientations.
const Traits::LocalBasisType &	localBasis () const
const Traits::LocalCoefficientsType &	localCoefficients () const
const Traits::LocalInterpolationType &	localInterpolation () const

Static Public Member Functions
static constexpr unsigned int	size ()
static constexpr GeometryType	type ()

Detailed Description

template<class D, class R, int dim, int k>
class Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >

Nédélec elements of the first kind for simplex elements.

These elements have been described in :

J.C. Nédélec, "Mixed finite elements in R^3", Numer.Math., 35(3):315-341,1980. DOI: http://dx.doi.org/10.1007/BF01396415

The order count starts at '1'. This is the counting used, e.g., by Nédélec himself, and by Kirby, Logg, Rognes, Terrel, "Common and unusual finite elements", https://doi.org/10.1007/978-3-642-23099-8_3

Note

These shape functions are implemented for the reference simplices only! The transformation to other simplices has to be done by the user. One way of doing that is using the implementation of the covariant Piola transform in globalvaluedlocalfinitelement.hh in dune-functions.

Template Parameters

D	Number type used for domain coordinates
R	Number type use for shape function values
dim	Dimension of the domain
k	Order of the Nedelec finite element (lowest is 1)

Member Typedef Documentation

Traits

template<class D , class R , int dim, int k>

using Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::Traits = LocalFiniteElementTraits<Impl::Nedelec1stKindSimplexLocalBasis<D,R,dim,k>, Impl::Nedelec1stKindSimplexLocalCoefficients<dim,k>, Impl::Nedelec1stKindSimplexLocalInterpolation<Impl::Nedelec1stKindSimplexLocalBasis<D,R,dim,k> > >

Constructor & Destructor Documentation

Nedelec1stKindSimplexLocalFiniteElement() [1/2]

template<class D , class R , int dim, int k>

Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::Nedelec1stKindSimplexLocalFiniteElement ( )

default

Default constructor.

Nedelec1stKindSimplexLocalFiniteElement() [2/2]

template<class D , class R , int dim, int k>

Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::Nedelec1stKindSimplexLocalFiniteElement ( std::bitset< dim *(dim+1)/2 >  s )

inline

Constructor with explicitly given edge orientations.

Parameters

s	Edge orientation indicator

Member Function Documentation

localBasis()

template<class D , class R , int dim, int k>

const Traits::LocalBasisType & Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::localBasis ( ) const

inline

localCoefficients()

template<class D , class R , int dim, int k>

const Traits::LocalCoefficientsType & Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::localCoefficients ( ) const

inline

localInterpolation()

template<class D , class R , int dim, int k>

const Traits::LocalInterpolationType & Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::localInterpolation ( ) const

inline

size()

template<class D , class R , int dim, int k>

static constexpr unsigned int Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::size ( )

inlinestaticconstexpr

type()

template<class D , class R , int dim, int k>

static constexpr GeometryType Dune::Nedelec1stKindSimplexLocalFiniteElement< D, R, dim, k >::type ( )

inlinestaticconstexpr

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

• nedelec1stkindsimplex.hh