Hello,
I upgraded my fenics-installation on ubuntu jaunty to the latest version
and observed some problems with lowest order Nedelec elements in 3D. Since
I was not sure, is I'm using the new Expression-Class properly I wrote
some simple 2D test cases and it seems that already the L^2-projection for
lowest order elements is wrong. In the attached sample code the value of
the projection does not converge to the value of the function. If I use in
contrast in Projection.ufl higher order Nedelec-spaces it converges.
Regards,
Holger
Projection.ufl:
W1F = FiniteElement("Nedelec 1st kind H(curl)", "triangle",0)
vL = VectorElement("Lagrange", "triangle", 3)
v = TestFunction(W1F)
u = TrialFunction(W1F)
f = Function(vL)
a = inner(v, u)*dx
L = inner(v,f)*dx
and
main.cpp:
#include <dolfin.h>
#include "Projection.h"
using namespace dolfin;
int main()
{
class Solution : public Expression
{
public:
Solution() : Expression(2,2) {}
void eval(double* values, const double* x) const
{
values[0] = 1;
values[1] = 0; //sin(DOLFIN_PI*x[0]);
}
};
UnitSquare mesh(2,2);
Solution solution;
for (unsigned int i=0; i<6; i++)
{
mesh.refine();
Projection::FunctionSpace VP(mesh);
Projection::BilinearForm m(VP,VP);
Projection::LinearForm LP(VP);
LP.f = solution;
VariationalProblem problemP(m,LP);
Function T(VP);
problemP.solve(T);
double x[2] = {0.123, 0.23441};
// Evaluate user-defined function f
double value[2] = {0.1,0.1};
solution.eval(&(value[0]), x);
info("exact value f(x) = (%g,%g)", value[0],value[1]);
// Evaluate discrete function g (projection of f)
double value2[2] = {0.1,0.1};
T.eval(&(value2[0]), x);
info("value of projection g(x) = (%g,%g)", value2[0],value2[1]);
}
return 0;}
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