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

The sinus product function – error analysis for the hybrid discontinuous Galerkin method.

The sinus product function – error analysis for the hybrid discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "cosinusprod.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
Float err_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
bool with_u = (argc <= 2) || argv[2] != string("-us");
bool with_sigma = ((argc <= 2) || argv[2] != string("-no-sigma")) && with_u;
field uh, lambda_h, sigma_h;
if (with_u) {
din >> catchmark("u") >> uh; // hdg or hho
} else {
din >> catchmark("us") >> uh; // hho
}
din >> catchmark("lambda") >> lambda_h;
if (with_sigma) {
din >> catchmark("sigma") >> sigma_h;
}
space Xh = uh.get_space();
geo omega = Xh.get_geo();
size_t k = Xh.degree();
size_t d = omega.dimension();
iopt.set_family(integrate_option::gauss);
iopt.set_order(3*(k+1)+4);
Float err_u_l2 = sqrt(integrate (omega, sqr(uh-u_exact(d)), iopt));
string opts = Xh.get_basis().option().stamp();
space Xh1 (omega, "P"+to_string(k+1)+"d"+opts);
field euh = lazy_interpolate (Xh1, uh-u_exact(d));
Float err_u_linf = euh.max_abs();
Float err_u_h1 = sqrt(integrate (omega, norm2(grad_h(euh)), iopt)
+ integrate (omega.sides(), (1/h_local())*sqr(jump(euh)), iopt));
derr << "err_u_l2 = " << err_u_l2 << endl
<< "err_u_linf = " << err_u_linf << endl
<< "err_u_h1 = " << err_u_h1 << endl;
if (with_sigma) {
Float err_sigma_l2 = sqrt(integrate (omega, norm2(sigma_h-grad_u(d)), iopt));
space Th1 (omega, "P"+to_string(k+1)+"d"+opts, "vector");
field esh = lazy_interpolate (Th1, sigma_h-grad_u(d));
Float err_sigma_linf = esh.max_abs();
derr << "err_sigma_l2 = " << err_sigma_l2 << endl
<< "err_sigma_linf = " << err_sigma_linf << endl;
}
if (!lambda_h.get_space().get_basis().option().is_trace_n()) {
space Mh = lambda_h.get_space();
trial lambda(Mh); test mu(Mh);
form ms = integrate(lambda*mu);
field kh = integrate(u_exact(d)*mu, iopt);
field ph_lambda(Mh);
problem pms (ms);
pms.solve (kh, ph_lambda);
Float err_lambda_l2 = sqrt(integrate (omega["sides"], h_local()*sqr(lambda_h-ph_lambda), iopt));
derr << "err_lambda_l2 = " << err_lambda_l2 << endl;
}
return (err_u_linf <= err_linf_expected) ? 0 : 1;
}
see the Float page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the geo page for the full documentation
see the problem 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
see the integrate_option page for the full documentation
void set_family(family_type type)
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
The cosinus product function.
The cosinus product function – its gradient.
int main()
Definition field2bb.cc:58
space_basic< T, M > Xh1
Definition field_expr.h:232
This file is part of Rheolef.
STL namespace.
rheolef - reference manual