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

The Mossolov problem for a circular pipe – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc,argv);
Float tol_u = (argc > 1) ? atof(argv[1]) : 1e-15;
Float tol_s = (argc > 2) ? atof(argv[2]) : 1e-15;
Float Bi, n;
field sigma_h, uh;
din >> catchmark("Bi") >> Bi
>> catchmark("n") >> n
>> catchmark("sigma") >> sigma_h
>> catchmark("u") >> uh;
const geo& omega = uh.get_geo();
Float meas_omega = integrate(uh.get_geo());
geo boundary = omega["boundary"];
const space& Xh = uh.get_space();
const space& Th = sigma_h.get_space();
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(3*Xh.degree());
Float err_u_l2 = sqrt(integrate (omega, sqr(uh - u(Bi,n)), iopt)/meas_omega);
Float err_u_h1 = sqrt(integrate (omega, norm2(grad(uh) - grad_u(Bi,n)), iopt)/meas_omega);
Float err_s_l2 = sqrt(integrate (omega, norm2(sigma_h - sigma(Bi,n)), iopt)/meas_omega);
space Xh1 (omega, "P" + itos(2*Xh.degree()));
space Th1 (omega, "P" + itos(2*Xh.degree()) + "d", "vector");
field euh = interpolate (Xh1, uh - u(Bi,n));
field esh = interpolate (Th1, sigma_h - sigma(Bi,n));
Float err_u_linf = euh.max_abs();
Float err_s_linf = esh.max_abs();
dout << "err_u_linf = " << err_u_linf << endl
<< "err_u_l2 = " << err_u_l2 << endl
<< "err_u_h1 = " << err_u_h1 << endl
<< "err_s_linf = " << err_s_linf << endl
<< "err_s_l2 = " << err_s_l2 << endl;
return (err_u_linf < tol_u) && (err_s_l2 < tol_s) ? 0 : 1;
}
see the Float page for the full documentation
see the field page for the full documentation
see the geo page for the full documentation
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
see the space page for the full documentation
space_basic< T, M > Xh1
Definition: field_expr.h:263
int main(int argc, char **argv)
The Mossolov problem for a circular pipe – exact solution.
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(const Expr &expr)
grad(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
Float u(const point &x)
tensor grad_u