Rheolef  7.1
an efficient C++ finite element environment
cosinusprod_error_hdg.cc

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_sigma = (argc <= 2) || argv[2] != string("-no-sigma");
field uh, lambda_h, sigma_h;
din >> catchmark("u") >> uh
>> 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();
integrate_option iopt;
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"+itos(k+1)+"d"+opts);
field euh = 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"+itos(k+1)+"d"+opts, "vector");
field esh = 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_restricted_to_sides()) {
space Mh = lambda_h.get_space();
trial lambda(Mh); test mu(Mh);
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
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
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.
int main(int argc, char **argv)
The cosinus product function – its gradient.
space_basic< T, M > Xh1
Definition: field_expr.h:263
This file is part of Rheolef.
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
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:202
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef - reference manual
g u_exact
Definition: taylor_exact.h:26
tensor grad_u