commute_rtd.cc

Discontinuous Raviart-Thomas L2 projection.

Discontinuous Raviart-Thomas L2 projection

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "cosinus_vector.h"
int main(int argc, char**argv) {
  environment rheolef (argc, argv);
  geo omega (argv[1]);
  size_t d = omega.dimension(),
         k = (argc > 2) ? atoi(argv[2]) : 0;
  space Vh (omega, "RT"+to_string(k)+"d"),
        Lh (omega, "P" +to_string(k)+"d"),
        Xh = Vh*Lh;
  trial x (Xh); test y (Xh);
  auto u = x[0], lambda = x[1];
  auto v = y[0], mu     = y[1];
  integrate_option iopt;
  iopt.invert = true;
  form  inv_a = integrate (dot(u,v) + div_h(v)*lambda + div_h(u)*mu, iopt);
  field lh = integrate (dot(u_exact(d),v) + div_u_exact(d)*mu),
        xh = inv_a*lh,
        p_Vh_u = xh[0],
        pi_h_u = lazy_interpolate(Vh,u_exact(d));
  dout << catchmark("p_Vh_u") << p_Vh_u
       << catchmark("pi_h_u") << pi_h_u;
}