Dune Core Modules (2.8.0)

Dune::HierarchicalSimplexP2LocalBasis< D, R, 3 > Class Template Reference

Hierarchical P2 basis in 3d. More...

#include <dune/localfunctions/hierarchical/hierarchicalp2/hierarchicalsimplexp2localbasis.hh>

Public Types

typedef LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 3 > > Traits
 export type traits for function signature
 

Public Member Functions

unsigned int size () const
 number of shape functions
 
void evaluateFunction (const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
 Evaluate all shape functions.
 
void evaluateJacobian (const typename Traits::DomainType &in, 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 all shape functions.
 
unsigned int order () const
 Polynomial order of the shape functions (2 in this case)
 

Detailed Description

template<class D, class R>
class Dune::HierarchicalSimplexP2LocalBasis< D, R, 3 >

Hierarchical P2 basis in 3d.

The shape functions are associated to the following points:

The functions are associated to points by:

  • \( f_0 \) ~ (0.0, 0.0, 0.0)
  • \( f_1 \) ~ (0.5, 0.0, 0.0)
  • \( f_2 \) ~ (1.0, 0.0, 0.0)
  • \( f_3 \) ~ (0.0, 0.5, 0.0)
  • \( f_4 \) ~ (0.5, 0.5, 0.0)
  • \( f_5 \) ~ (0.0, 1.0, 0.0)
  • \( f_6 \) ~ (0.0, 0.0, 0.5)
  • \( f_7 \) ~ (0.5, 0.0, 0.5)
  • \( f_8 \) ~ (0.0, 0.5, 0.5)
  • \( f_9 \) ~ (0.0, 0.0, 1.0)
Template Parameters
DType to represent the field in the domain.
RType to represent the field in the range.

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