Rheolef  7.2
an efficient C++ finite element environment
convect_error.cc

Convection-diffusion equation by the method of characteristics – error analysis.

Convection-diffusion equation by the method of characteristics – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "rotating-hill.h"
int main (int argc, char **argv) {
environment rheolef (argc,argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-10;
din >> catchmark("nu") >> nu;
branch get ("t","phi");
branch put ("t","phi_h","pi_h_phi");
derr << "# t\terror_l2\terror_linf" << endl;
field phi_h;
Float err_l2_l2 = 0;
Float err_linf_linf = 0;
for (Float t = 0, t_prec = 0; din >> get (t, phi_h); t_prec = t) {
const space& Xh = phi_h.get_space();
size_t d = Xh.get_geo().dimension();
field pi_h_phi = lazy_interpolate (Xh, phi(d,nu,t));
trial phi (Xh); test psi (Xh);
field eh = phi_h - pi_h_phi;
Float err_l2 = sqrt(m(eh,eh));
Float err_linf = eh.max_abs();
err_l2_l2 += sqr(err_l2)*(t - t_prec);
err_linf_linf = max(err_linf_linf, err_linf);
dout << put (t, phi_h, pi_h_phi);
derr << t << "\t" << err_l2 << "\t" << err_linf << endl;
}
derr << "# error_l2_l2 = " << sqrt(err_l2_l2) << endl;
derr << "# error_linf_linf = " << err_linf_linf << endl;
return (err_linf_linf <= tol) ? 0 : 1;
}
Float phi(const point &nu, Float a, Float b)
see the Float page for the full documentation
see the branch page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:121
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
int main(int argc, char **argv)
This file is part of Rheolef.
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: field.h:871
void put(std::ostream &out, std::string name, const tiny_matrix< T > &a)
Definition: tiny_lu.h:155
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&!is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:211
STL namespace.
rheolef - reference manual
Convection-diffusion equation – the rotating hill benchmark.
Definition: nu.h:26
Definition: phi.h:25