dune-localfunctions  2.2.1
Public Types | Public Member Functions | Static Protected Member Functions | List of all members
Dune::RefinedP1LocalBasis< D, R, 1 > Class Template Reference

Uniformly refined linear Lagrange shape functions in 1D. More...

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

Inheritance diagram for Dune::RefinedP1LocalBasis< D, R, 1 >:
Dune::RefinedSimplexLocalBasis< D, 1 >

Public Types

typedef LocalBasisTraits< D,
1, Dune::FieldVector< D, 1 >
, R, 1, Dune::FieldVector< R, 1 >
, Dune::FieldMatrix< R, 1, 1 > > 
Traits
 export type traits for function signature More...
 

Public Member Functions

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

Static Protected Member Functions

static int getSubElement (const FieldVector< D, 2 > &global)
 Get the number of the subelement containing a given point. More...
 
static void getSubElement (const FieldVector< D, 1 > &global, int &subElement, FieldVector< D, 1 > &local)
 Get local coordinates in the subelement. More...
 

Detailed Description

template<class D, class R>
class Dune::RefinedP1LocalBasis< D, R, 1 >

Uniformly refined linear Lagrange shape functions in 1D.

1D IMPLEMENTATION IS NOT TESTED (the LocalElement for 1D does not exist due to lack of P21D elements)

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) f_1 ~ (1.0) f_2 ~ (0.5)

Template Parameters
DType to represent the field in the domain.
RType to represent the field in the range.

Member Typedef Documentation

template<class D , class R >
typedef LocalBasisTraits<D,1,Dune::FieldVector<D,1>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,1> > Dune::RefinedP1LocalBasis< D, R, 1 >::Traits

export type traits for function signature

Member Function Documentation

template<class D , class R >
void Dune::RefinedP1LocalBasis< D, R, 1 >::evaluateFunction ( const typename Traits::DomainType in,
std::vector< typename Traits::RangeType > &  out 
) const
inline

Evaluate all shape functions.

template<class D , class R >
void Dune::RefinedP1LocalBasis< D, R, 1 >::evaluateJacobian ( const typename Traits::DomainType in,
std::vector< typename Traits::JacobianType > &  out 
) const
inline

Evaluate Jacobian of all shape functions.

template<class D >
static int Dune::RefinedSimplexLocalBasis< D, 1 >::getSubElement ( const FieldVector< D, 2 > &  global)
inlinestaticprotectedinherited

Get the number of the subelement containing a given point.

The subelements are ordered according to

0       1

|----—:----—|

Parameters
[in]globalCoordinates in the reference element
Returns
Number of the subtriangle containing global
template<class D >
static void Dune::RefinedSimplexLocalBasis< D, 1 >::getSubElement ( const FieldVector< D, 1 > &  global,
int &  subElement,
FieldVector< D, 1 > &  local 
)
inlinestaticprotectedinherited

Get local coordinates in the subelement.

Parameters
[in]globalCoordinates in the reference element
[out]subElementNumber of the subelement containing global
[out]localThe local coordinates in the subelement
template<class D , class R >
unsigned int Dune::RefinedP1LocalBasis< D, R, 1 >::order ( ) const
inline

Polynomial order of the shape functions Doesn't really apply: these shape functions are only piecewise linear.

template<class D , class R >
unsigned int Dune::RefinedP1LocalBasis< D, R, 1 >::size ( ) const
inline

number of shape functions


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