dune-localfunctions  2.2.1
Public Types | Public Member Functions | List of all members
Dune::Pk2DLocalBasis< D, R, k > Class Template Reference

Lagrange shape functions of arbitrary order on the reference triangle. More...

#include <dune/localfunctions/lagrange/pk2d/pk2dlocalbasis.hh>

Public Types

enum  { N = (k+1)*(k+2)/2 }
 Export the number of degrees of freedom. More...
 
enum  { O = k }
 Export the element order OS: Surprising that we need to export this both statically and dynamically! More...
 
typedef LocalBasisTraits< D,
2, Dune::FieldVector< D, 2 >
, R, 1, Dune::FieldVector< R, 1 >
, Dune::FieldMatrix< R, 1, 2 > > 
Traits
 

Public Member Functions

 Pk2DLocalBasis ()
 Standard constructor. More...
 
unsigned int size () const
 number of shape functions More...
 
void evaluateFunction (const typename Traits::DomainType &x, std::vector< typename Traits::RangeType > &out) const
 Evaluate all shape functions. More...
 
void evaluateJacobian (const typename Traits::DomainType &x, std::vector< typename Traits::JacobianType > &out) const
 Evaluate Jacobian of all shape functions. More...
 
unsigned int order () const
 Polynomial order of the shape functions. More...
 

Detailed Description

template<class D, class R, unsigned int k>
class Dune::Pk2DLocalBasis< D, R, k >

Lagrange shape functions of arbitrary order on the reference triangle.

Lagrange shape functions of arbitrary order have the property that $\hat\phi^i(x_j) = \delta_{i,j}$ for certain points $x_j$.

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

Member Typedef Documentation

template<class D , class R , unsigned int k>
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,2> > Dune::Pk2DLocalBasis< D, R, k >::Traits

Member Enumeration Documentation

template<class D , class R , unsigned int k>
anonymous enum

Export the number of degrees of freedom.

Enumerator
N 
template<class D , class R , unsigned int k>
anonymous enum

Export the element order OS: Surprising that we need to export this both statically and dynamically!

Enumerator
O 

Constructor & Destructor Documentation

template<class D , class R , unsigned int k>
Dune::Pk2DLocalBasis< D, R, k >::Pk2DLocalBasis ( )
inline

Standard constructor.

Member Function Documentation

template<class D , class R , unsigned int k>
void Dune::Pk2DLocalBasis< D, R, k >::evaluateFunction ( const typename Traits::DomainType x,
std::vector< typename Traits::RangeType > &  out 
) const
inline

Evaluate all shape functions.

References Dune::Pk2DLocalBasis< D, R, k >::N.

template<class D , class R , unsigned int k>
void Dune::Pk2DLocalBasis< D, R, k >::evaluateJacobian ( const typename Traits::DomainType x,
std::vector< typename Traits::JacobianType > &  out 
) const
inline

Evaluate Jacobian of all shape functions.

References Dune::Pk2DLocalBasis< D, R, k >::N.

template<class D , class R , unsigned int k>
unsigned int Dune::Pk2DLocalBasis< D, R, k >::order ( ) const
inline

Polynomial order of the shape functions.

template<class D , class R , unsigned int k>
unsigned int Dune::Pk2DLocalBasis< D, R, k >::size ( ) const
inline

number of shape functions

References Dune::Pk2DLocalBasis< D, R, k >::N.


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