dune-localfunctions
2.2.1
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Uniformly refined linear Lagrange shape functions on the triangle. More...
#include <dune/localfunctions/refined/refinedp1/refinedp1localbasis.hh>
Public Types | |
typedef LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 > , R, 1, Dune::FieldVector< R, 1 > , Dune::FieldMatrix< R, 1, 2 > > | Traits |
export type traits for function signature More... | |
Public Member Functions | |
unsigned int | size () const |
number of shape functions More... | |
void | evaluateFunction (const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const |
Evaluate all shape functions. More... | |
void | evaluateJacobian (const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const |
Evaluate Jacobian of all shape functions. More... | |
unsigned int | order () const |
Polynomial order of the shape functions Doesn't really apply: these shape functions are only piecewise linear. More... | |
Static Protected Member Functions | |
static int | getSubElement (const FieldVector< D, 2 > &global) |
Get the number of the subtriangle containing a given point. More... | |
static void | getSubElement (const FieldVector< D, 2 > &global, int &subElement, FieldVector< D, 2 > &local) |
Get local coordinates in the subtriangle. More... | |
Uniformly refined linear Lagrange shape functions on the triangle.
This shape function set mimicks the P1 shape functions that you would get on a uniformly refined grid. Hence these shape functions are only piecewise linear! The data layout is identical to P2 shape functions.
Shape functions like these are necessary for hierarchical error estimators for certain nonlinear problems.
The functions are associated to points by:
f_0 ~ (0.0, 0.0) f_1 ~ (0.5, 0.0) f_2 ~ (1.0, 0.0) f_3 ~ (0.0, 0.5) f_4 ~ (0.5, 0.5) f_5 ~ (0.0, 1.0)
D | Type to represent the field in the domain. |
R | Type to represent the field in the range. |
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,2> > Dune::RefinedP1LocalBasis< D, R, 2 >::Traits |
export type traits for function signature
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inline |
Evaluate all shape functions.
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inline |
Evaluate Jacobian of all shape functions.
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inlinestaticprotectedinherited |
Get the number of the subtriangle containing a given point.
The triangles are ordered according to
|\ |2\ |--\ |\3|\ |0\|1\ ------
[in] | global | Coordinates in the reference triangle |
global
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inlinestaticprotectedinherited |
Get local coordinates in the subtriangle.
[in] | global | Coordinates in the reference triangle |
[out] | subElement | Number of the subtriangle containing global |
[out] | local | The local coordinates in the subtriangle |
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inline |
Polynomial order of the shape functions Doesn't really apply: these shape functions are only piecewise linear.
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inline |
number of shape functions