dune-localfunctions 2.10
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Public Types | Public Member Functions | Static Public Member Functions | List of all members
Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim > Class Template Reference

Linear Lagrange functions enriched with quadratic edge bubble functions and an element bubble function. More...

#include <dune/localfunctions/hierarchical/hierarchicalp2withelementbubble.hh>

Public Types

using LocalBasisType = HierarchicalSimplexP2WithElementBubbleLocalBasis< D, R, dim >
 Type of the local basis.
 
using LocalCoefficientsType = HierarchicalSimplexP2WithElementBubbleLocalCoefficients< dim >
 Type of the local coefficients.
 
using LocalInterpolationType = HierarchicalSimplexP2WithElementBubbleLocalInterpolation< LocalBasisType, dim >
 Type of the local interpolation.
 
using Traits = LocalFiniteElementTraits< LocalBasisType, LocalCoefficientsType, LocalInterpolationType >
 Traits type that specifies the local basis, coefficients, and interpolation type.
 

Public Member Functions

const LocalBasisTypelocalBasis () const
 Returns the local basis, i.e., the set of shape functions.
 
const LocalCoefficientsTypelocalCoefficients () const
 Returns the assignment of the degrees of freedom to the element subentities.
 
const LocalInterpolationTypelocalInterpolation () const
 Returns object that evaluates degrees of freedom.
 

Static Public Member Functions

static constexpr std::size_t size () noexcept
 Returns the number of shape functions in this finite-element.
 
static constexpr GeometryType type () noexcept
 Returns the type of the geometry the finite-element is attached to.
 

Detailed Description

template<class D, class R, int dim>
class Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >

Linear Lagrange functions enriched with quadratic edge bubble functions and an element bubble function.

The set of basis functions contains the classical Lagrange basis functions of order 1, i.e., the barycentric coordinates, edge bubble functions as the product of two linear functions, and a single element bubble function that vanishes on all faces of the element. The element bubble function is the product of all linear basis functions and thus has polynomial order dim+1.

Note
The implementation here is restricted to simplex elements.
Template Parameters
DType to represent the field in the domain.
RType to represent the field in the range.
dimDimension of the domain.

Member Typedef Documentation

◆ LocalBasisType

template<class D , class R , int dim>
using Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::LocalBasisType = HierarchicalSimplexP2WithElementBubbleLocalBasis<D,R,dim>

Type of the local basis.

◆ LocalCoefficientsType

template<class D , class R , int dim>
using Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::LocalCoefficientsType = HierarchicalSimplexP2WithElementBubbleLocalCoefficients<dim>

Type of the local coefficients.

◆ LocalInterpolationType

template<class D , class R , int dim>
using Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::LocalInterpolationType = HierarchicalSimplexP2WithElementBubbleLocalInterpolation<LocalBasisType,dim>

Type of the local interpolation.

◆ Traits

Traits type that specifies the local basis, coefficients, and interpolation type.

Member Function Documentation

◆ localBasis()

template<class D , class R , int dim>
const LocalBasisType & Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::localBasis ( ) const
inline

Returns the local basis, i.e., the set of shape functions.

◆ localCoefficients()

template<class D , class R , int dim>
const LocalCoefficientsType & Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::localCoefficients ( ) const
inline

Returns the assignment of the degrees of freedom to the element subentities.

◆ localInterpolation()

template<class D , class R , int dim>
const LocalInterpolationType & Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::localInterpolation ( ) const
inline

Returns object that evaluates degrees of freedom.

◆ size()

template<class D , class R , int dim>
static constexpr std::size_t Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::size ( )
inlinestaticconstexprnoexcept

Returns the number of shape functions in this finite-element.

◆ type()

template<class D , class R , int dim>
static constexpr GeometryType Dune::HierarchicalP2WithElementBubbleLocalFiniteElement< D, R, dim >::type ( )
inlinestaticconstexprnoexcept

Returns the type of the geometry the finite-element is attached to.


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