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

The combustion problem – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc,argv);
bool is_upper = (argc > 1) && (argv[1][0] == '1');
bool is_crit = (argc > 1) && (argv[1][0] == 'c');
Float tol = (argc > 2) ? atof(argv[2]) : 1e-15;
Float lambda_h;
field uh;
din >> catchmark("lambda") >> lambda_h
>> catchmark("u") >> uh;
Float lambda = (is_crit ? lambda_c() : lambda_h);
const geo& omega = uh.get_geo();
const space& Xh = uh.get_space();
field pi_h_u = lazy_interpolate (Xh, u_exact(lambda,is_upper));
field eh = pi_h_u - uh;
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*Xh.degree()+1);
Float err_l2
= sqrt(integrate(omega, norm2(uh - u_exact(lambda,is_upper)), iopt));
Float err_h1
= sqrt(integrate(omega, norm2(grad(uh)-grad_u(lambda,is_upper)), iopt));
Float err_linf = eh.max_abs();
dout << "err_linf = " << err_linf << endl
<< "err_l2 = " << err_l2 << endl
<< "err_h1 = " << err_h1 << endl;
return (err_h1 < tol) ? 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(cin)
see the diststream page for the full documentation
Definition: diststream.h:464
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
see the space page for the full documentation
int main(int argc, char **argv)
The combustion problem – its exact solution.
Float lambda_c()
Definition: lambda_c.h:44
This file is part of Rheolef.
std::enable_if< details::has_field_rdof_interface< 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
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
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
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef - reference manual
g u_exact
Definition: taylor_exact.h:26