dune-localfunctions: Dune::Pk2DLocalBasis< D, R, k > Class Template Reference

dune-localfunctions 2.2.1

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

D	Type to represent the field in the domain.
R	Type to represent the field in the range.
k	Polynomial 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:

pk2dlocalbasis.hh