dune-localfunctions  2.5.0
Public Types | Public Member Functions | List of all members
Dune::Pk1DLocalBasis< D, R, k > Class Template Reference

Lagrange shape functions of arbitrary order on the 1D reference triangle. More...

#include <dune/localfunctions/lagrange/pk1d/pk1dlocalbasis.hh>

Public Types

enum  { N = k+1 }
 Export the number of degrees of freedom. More...
 
enum  { O = k }
 Export the element order. More...
 
typedef LocalBasisTraits< D, 1, Dune::FieldVector< D, 1 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 1 > > Traits
 

Public Member Functions

 Pk1DLocalBasis ()
 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...
 
void partial (const std::array< unsigned int, 1 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
 Evaluate partial derivatives of any order 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::Pk1DLocalBasis< D, R, k >

Lagrange shape functions of arbitrary order on the 1D 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

§ Traits

template<class D, class R, unsigned int k>
typedef LocalBasisTraits<D, 1, Dune::FieldVector<D,1>, R, 1, Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,1> > Dune::Pk1DLocalBasis< D, R, k >::Traits

Member Enumeration Documentation

§ anonymous enum

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

Export the number of degrees of freedom.

Enumerator

§ anonymous enum

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

Export the element order.

Enumerator

Constructor & Destructor Documentation

§ Pk1DLocalBasis()

template<class D, class R, unsigned int k>
Dune::Pk1DLocalBasis< D, R, k >::Pk1DLocalBasis ( )
inline

Standard constructor.

Member Function Documentation

§ evaluateFunction()

template<class D, class R, unsigned int k>
void Dune::Pk1DLocalBasis< D, R, k >::evaluateFunction ( const typename Traits::DomainType x,
std::vector< typename Traits::RangeType > &  out 
) const
inline

Evaluate all shape functions.

§ evaluateJacobian()

template<class D, class R, unsigned int k>
void Dune::Pk1DLocalBasis< D, R, k >::evaluateJacobian ( const typename Traits::DomainType x,
std::vector< typename Traits::JacobianType > &  out 
) const
inline

Evaluate Jacobian of all shape functions.

§ order()

template<class D, class R, unsigned int k>
unsigned int Dune::Pk1DLocalBasis< D, R, k >::order ( ) const
inline

Polynomial order of the shape functions.

§ partial()

template<class D, class R, unsigned int k>
void Dune::Pk1DLocalBasis< D, R, k >::partial ( const std::array< unsigned int, 1 > &  order,
const typename Traits::DomainType in,
std::vector< typename Traits::RangeType > &  out 
) const
inline

Evaluate partial derivatives of any order of all shape functions.

Parameters
orderOrder of the partial derivatives, in the classic multi-index notation
inPosition where to evaluate the derivatives
[out]outReturn value: the desired partial derivatives

§ size()

template<class D, class R, unsigned int k>
unsigned int Dune::Pk1DLocalBasis< D, R, k >::size ( ) const
inline

number of shape functions


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