3 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
10 #include <dune/common/fmatrix.hh>
12 #include "../../common/localbasis.hh"
25 template<
class D,
class R>
31 R,2,Dune::FieldVector<R,2>,
37 for (
size_t i=0; i<3; i++)
48 for (
size_t i=0; i<3; i++)
49 sign_[i] = s[i] ? -1.0 : 1.0;
65 std::vector<typename Traits::RangeType>& out)
const
69 out[0][0] = sign_[0]*(-2*in[0]*in[1] + in[0]*in[0]);
70 out[0][1] = sign_[0]*(-1 + 6*in[1] -2*in[0]*in[1] - 5*in[1]*in[1]);
72 out[1][0] = 1.5*in[0] + 3*in[0]*in[1] - 4.5*in[0]*in[0];
73 out[1][1] = -3 + 6*in[0] + 10.5*in[1] - 15*in[0]*in[1] - 7.5*in[1]*in[1];
75 out[2][0] = sign_[0]*(-7.5*in[0] + 5*in[0]*in[1] + 12.5*in[0]*in[0]);
76 out[2][1] = sign_[0]*(-5 + 30*in[0] + 7.5*in[1] - 25*in[0]*in[1] - 30*in[0]*in[0] - 2.5*in[1]*in[1]);
80 out[3][0] = sign_[1]*(-1 + 6*in[0] - 2*in[0]*in[1] - 5*in[0]*in[0]);
81 out[3][1] = sign_[1]*(-2*in[0]*in[1] + in[1]*in[1]);
83 out[4][0] = 3 - 10.5*in[0] - 6*in[1] + 15*in[0]*in[1] + 7.5*in[0]*in[0];
84 out[4][1] = -1.5*in[1] - 3*in[0]*in[1] + 4.5*in[1]*in[1];
86 out[5][0] = sign_[1]*(-5 + 7.5*in[0] + 30*in[1] - 25*in[0]*in[1] - 2.5*in[0]*in[0] - 30*in[1]*in[1]);
87 out[5][1] = sign_[1]*(-7.5*in[1] + 5*in[0]*in[1] + 12.5*in[1]*in[1]);
91 out[6][0] = sign_[2]*(-3*in[0] + 4*in[0]*in[1] + 4*in[0]*in[0]);
92 out[6][1] = sign_[2]*(-3*in[1] + 4*in[0]*in[1] + 4*in[1]*in[1]);
94 out[7][0] = -3*in[0] + 6*in[0]*in[0];
95 out[7][1] = 3*in[1] - 6*in[1]*in[1];
97 out[8][0] = sign_[2]*(-10*in[0]*in[1] + 5*in[0]*in[0]);
98 out[8][1] = sign_[2]*(-10*in[0]*in[1] + 5*in[1]*in[1]);
102 out[9][0] = 18*in[0] - 12*in[0]*in[1] - 18*in[0]*in[0];
103 out[9][1] = 6*in[1] - 12*in[0]*in[1] - 6*in[1]*in[1];
105 out[10][0] = 6*in[0] - 12*in[0]*in[1] - 6*in[0]*in[0];
106 out[10][1] = 18*in[1] - 12*in[0]*in[1] - 18*in[1]*in[1];
108 out[11][0] = 90*in[0] - 180*in[0]*in[1] - 90*in[0]*in[0];
109 out[11][1] = -90*in[1] + 180*in[0]*in[1] + 90*in[1]*in[1];
119 std::vector<typename Traits::JacobianType>& out)
const
123 out[0][0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
124 out[0][0][1] = sign_[0]*(-2*in[0]);
126 out[0][1][0] = sign_[0]*(-2*in[1]);
127 out[0][1][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
130 out[1][0][0] = 1.5 + 3*in[1] - 9*in[0];
131 out[1][0][1] = 3*in[0];
133 out[1][1][0] = 6 - 15*in[1];
134 out[1][1][1] = 10.5 - 15*in[0] - 15*in[1];
137 out[2][0][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
138 out[2][0][1] = sign_[0]*(5*in[0]);
140 out[2][1][0] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
141 out[2][1][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
145 out[3][0][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
146 out[3][0][1] = sign_[1]*(-2*in[0]);
148 out[3][1][0] = sign_[1]*(-2*in[1]);
149 out[3][1][1] = sign_[1]*(-2*in[0] + 2*in[1]);
152 out[4][0][0] = -10.5 + 15*in[1] + 15*in[0];
153 out[4][0][1] = -6 + 15*in[0];
155 out[4][1][0] = -3*in[1];
156 out[4][1][1] = -1.5 - 3*in[0] + 9*in[1];
159 out[5][0][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
160 out[5][0][1] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
162 out[5][1][0] = sign_[1]*(5*in[1]);
163 out[5][1][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
167 out[6][0][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
168 out[6][0][1] = sign_[2]*(4*in[0]);
170 out[6][1][0] = sign_[2]*(4*in[1]);
171 out[6][1][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
174 out[7][0][0] = -3 + 12*in[0];
178 out[7][1][1] = 3 - 12*in[1];
181 out[8][0][0] = sign_[2]*(-10*in[1] + 10*in[0]);
182 out[8][0][1] = sign_[2]*(-10*in[0]);
184 out[8][1][0] = sign_[2]*(-10*in[1]);
185 out[8][1][1] = sign_[2]*(-10*in[0] + 10*in[1]);
188 out[9][0][0] = 18 - 12*in[1] - 36*in[0];
189 out[9][0][1] = -12*in[0];
191 out[9][1][0] = -12*in[1];
192 out[9][1][1] = 6 - 12*in[0] - 12*in[1];
194 out[10][0][0] = 6 - 12*in[1] - 12*in[0];
195 out[10][0][1] = -12*in[0];
197 out[10][1][0] = -12*in[1];
198 out[10][1][1] = 18 - 12*in[0] - 36*in[1];
200 out[11][0][0] = 90 - 180*in[1] - 180*in[0];
201 out[11][0][1] = -180*in[0];
203 out[11][1][0] = 180*in[1];
204 out[11][1][1] = -90 + 180*in[0] + 180*in[1];
214 std::array<R,3> sign_;
217 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
BDM2Simplex2DLocalBasis(std::bitset< 3 > s)
Make set number s, where 0 <= s < 8.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:46
unsigned int size() const
number of shape functions
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:53
BDM2Simplex2DLocalBasis()
Standard constructor.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:35
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:118
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 2, Dune::FieldVector< R, 2 >, Dune::FieldMatrix< R, 2, 2 > > Traits
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:32
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:64
unsigned int order() const
Polynomial order of the shape functions.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:208
First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
Definition: brezzidouglasmarini2simplex2dlocalbasis.hh:26
D DomainType
domain type
Definition: localbasis.hh:49