Dune::RefinedP1LocalBasis< D, R, 2 > Class Template Reference

Uniformly refined linear Lagrange shape functions on the triangle. More...

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

Public Types
typedef LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 2 > >	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, 2 > &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, 2 > &global)
	Get the number of the subtriangle containing a given point. More...
static void	getSubElement (const FieldVector< D, 2 > &global, int &subElement, FieldVector< D, 2 > &local)
	Get local coordinates in the subtriangle. More...

Detailed Description

template<class D, class R>
class Dune::RefinedP1LocalBasis< D, R, 2 >

Uniformly refined linear Lagrange shape functions on the triangle.

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) f_1 ~ (0.5, 0.0) f_2 ~ (1.0, 0.0) f_3 ~ (0.0, 0.5) f_4 ~ (0.5, 0.5) f_5 ~ (0.0, 1.0)

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, 2 >::getSubElement ( const FieldVector< D, 2 > &  global )

inlinestaticprotectedinherited

Get the number of the subtriangle containing a given point.

The triangles are ordered according to

|\
|2\
|--\
|\3|\
|0\|1\
------

Parameters

[in]

global

Coordinates in the reference triangle

Returns

Number of the subtriangle containing global

getSubElement() [2/2]

template<class D >

static void Dune::RefinedSimplexLocalBasis< D, 2 >::getSubElement ( const FieldVector< D, 2 > &  global, int &  subElement, FieldVector< D, 2 > &  local  )

inlinestaticprotectedinherited

Get local coordinates in the subtriangle.

Parameters

[in]	global	Coordinates in the reference triangle
[out]	subElement	Number of the subtriangle containing global
[out]	local	The local coordinates in the subtriangle

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

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