3#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALINTERPOLATION_HH
8#include <dune/geometry/quadraturerules.hh>
29 sign0 = sign1 = sign2 = 1.0;
40 sign0 = sign1 = sign2 = 1.0;
58 n2[0] = 1.0/sqrt(2.0);
59 n2[1] = 1.0/sqrt(2.0);
60 c0 = 0.5*n0[0] - 1.0*n0[1];
61 c1 = -1.0*n1[0] + 0.5*n1[1];
62 c2 = 0.5*n2[0] + 0.5*n2[1];
73 template<
typename F,
typename C>
77 typedef typename LB::Traits::RangeFieldType Scalar;
79 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
82 fill(out.begin(), out.end(), 0.0);
85 const Dune::QuadratureRule<Scalar,1>& rule = Dune::QuadratureRules<Scalar,1>::rule(Dune::GeometryTypes::simplex(1), qOrder);
87 for (
typename Dune::QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it)
89 Scalar qPos = it->position();
90 typename LB::Traits::DomainType localPos;
95 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0/c0;
96 out[3] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight()/c0;
101 out[1] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1/c1;
102 out[4] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight()/c1;
104 localPos[0] = 1.0 - qPos;
107 out[2] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2/c2;
108 out[5] += (y[0]*n2[0] + y[1]*n2[1])*(2.0*qPos - 1.0)*it->weight()/c2;
113 typename LB::Traits::RangeFieldType sign0,sign1,sign2;
114 typename LB::Traits::DomainType n0,n1,n2;
115 typename LB::Traits::RangeFieldType c0,c1,c2;
Definition: bdfmcube.hh:16
First order Brezzi-Douglas-Marini shape functions on the reference triangle.
Definition: brezzidouglasmarini1simplex2dlocalinterpolation.hh:23
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: brezzidouglasmarini1simplex2dlocalinterpolation.hh:74
BDM1Simplex2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini1simplex2dlocalinterpolation.hh:37
BDM1Simplex2DLocalInterpolation()
Standard constructor.
Definition: brezzidouglasmarini1simplex2dlocalinterpolation.hh:27