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

The Helmholtz problem on a surface – error analysis

#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "sphere.icc"
int main (int argc, char**argv) {
environment rheolef(argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e+38;
field uh; din >> uh;
const space& Wh = uh.get_space();
trial u (Wh); test v (Wh);
form m = integrate (u*v);
size_t d = Wh.get_geo().dimension();
field pi_h_u = interpolate(Wh, u_exact(d));
field eh = uh - pi_h_u;
dout << "err_l2 " << sqrt(m(eh,eh)) << endl
<< "err_h1 " << sqrt(a(eh,eh)) << endl
<< "err_linf " << eh.max_abs() << endl;
return (eh.max_abs() < tol) ? 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
T max_abs() const
Definition: field.h:731
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
field_basic< T, M > eh
int main(int argc, char **argv)
rheolef::details::is_vec dot
This file is part of Rheolef.
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_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
idiststream din(cin)
see the diststream 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
rheolef - reference manual
The level set function for the sphere geometry.
Definition: leveque.h:25
g u_exact
Definition: taylor_exact.h:26
Float u(const point &x)