Dune Core Modules (2.6.0)

Dune::Pk3DLocalBasis< D, R, k > Class Template Reference

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

#include <dune/localfunctions/lagrange/pk3d/pk3dlocalbasis.hh>

Public Member Functions

 Pk3DLocalBasis ()
 Standard constructor.
 
unsigned int size () const
 number of shape functions
 
void evaluateFunction (const typename Traits::DomainType &x, std::vector< typename Traits::RangeType > &out) const
 Evaluate all shape functions.
 
void evaluateJacobian (const typename Traits::DomainType &x, std::vector< typename Traits::JacobianType > &out) const
 Evaluate Jacobian of all shape functions.
 
void partial (const std::array< unsigned int, 3 > &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.
 

Detailed Description

template<class D, class R, unsigned int k>
class Dune::Pk3DLocalBasis< D, R, k >

Lagrange shape functions of arbitrary order on the reference tetrahedron.

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 Function Documentation

◆ partial()

template<class D , class R , unsigned int k>
void Dune::Pk3DLocalBasis< D, R, k >::partial ( const std::array< unsigned int, 3 > &  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

References Dune::Hybrid::accumulate(), DUNE_THROW, Dune::Pk3DLocalBasis< D, R, k >::evaluateFunction(), and Dune::Pk3DLocalBasis< D, R, k >::order().


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