Dune::RefinedP1LocalBasis< D, R, 3 > Class Template Reference

Uniformly refined linear Lagrange shape functions on the 3D-simplex (tetrahedron). More...

#include <dune/localfunctions/refined/refinedp1/refinedp1localbasis.hh>

Public Types
typedef LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 3 > >	Traits
	export type traits for function signature

Public Member Functions
unsigned int	size () const
	number of shape functions
void	evaluateFunction (const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
	Evaluate all shape functions.
void	evaluateJacobian (const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
	Evaluate Jacobian of all shape functions.
void	partial (const std::array< unsigned int, 3 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
	Evaluate partial derivatives of all shape functions.
unsigned int	order () const
	Polynomial order of the shape functions Doesn't really apply: these shape functions are only piecewise linear.

Static Protected Member Functions
static int	getSubElement (const FieldVector< D, 3 > &global)
	Get the number of the subsimplex containing a given point in the reference element. More...
static void	getSubElement (const FieldVector< D, 3 > &global, int &subElement, FieldVector< D, 3 > &local)
	Get local coordinates in the subsimplex. More...

Detailed Description

template<class D, class R>
class Dune::RefinedP1LocalBasis< D, R, 3 >

Uniformly refined linear Lagrange shape functions on the 3D-simplex (tetrahedron).

This shape function set mimicks the P1 shape functions that you would get on a uniformly refined grid. Hence these shape functions are only piecewise linear! The data layout is identical to P2 shape functions.

Shape functions like these are necessary for hierarchical error estimators for certain nonlinear problems.

The functions are associated to points by:

f_0 ~ (0.0, 0.0, 0.0) f_1 ~ (1.0, 0.0, 0.0) f_2 ~ (0.0, 1.0, 0.0) f_3 ~ (0.0, 0.0, 1.0) f_4 ~ (0.5, 0.0, 0.0) f_5 ~ (0.5, 0.5, 0.0) f_6 ~ (0.0, 0.5, 0.0) f_7 ~ (0.0, 0.0, 0.5) f_8 ~ (0.5, 0.0, 0.5) f_9 ~ (0.0, 0.5, 0.5)

Template Parameters

D	Type to represent the field in the domain.
R	Type to represent the field in the range.

Member Function Documentation

getSubElement() [1/2]

template<class D >

static int Dune::RefinedSimplexLocalBasis< D, 3 >::getSubElement ( const FieldVector< D, 3 > &  global )

inlinestaticprotectedinherited

Get the number of the subsimplex containing a given point in the reference element.

Defining the following points in the reference simplex

0: (0.0, 0.0, 0.0) 1: (1.0, 0.0, 0.0) 2: (0.0, 1.0, 0.0) 3: (0.0, 0.0, 1.0) 4: (0.5, 0.0, 0.0) 5: (0.5, 0.5, 0.0) 6: (0.0, 0.5, 0.0) 7: (0.0, 0.0, 0.5) 8: (0.5, 0.0, 0.5) 9: (0.0, 0.5, 0.5)

The subsimplices are numbered according to

0: 0467 - 1: 4158 |_ "cut off" vertices 2: 6529 | 3: 7893 -

4: 6487 - 5: 4568 |_ octahedron partition 6: 6897 | 7: 6895 -

Parameters

[in]

global

Coordinates in the reference simplex

Returns

Number of the subsimplex containing global

References DUNE_THROW.

getSubElement() [2/2]

template<class D >

static void Dune::RefinedSimplexLocalBasis< D, 3 >::getSubElement ( const FieldVector< D, 3 > &  global, int &  subElement, FieldVector< D, 3 > &  local  )

inlinestaticprotectedinherited

Get local coordinates in the subsimplex.

Parameters

[in]	global	Coordinates in the reference simplex
[out]	subElement	Number of the subsimplex containing global
[out]	local	The local coordinates in the subsimplex

References DUNE_THROW.

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

• dune/localfunctions/refined/refinedp1/refinedp1localbasis.hh