laplace_s_error.cc
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#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "torus.icc"
int main (int argc, char**argv) {
environment rheolef (argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-7;
field uh;
din >> uh;
const space& Wh = uh.get_space();
field pi_h_u = interpolate(Wh, u_exact());
field eh = uh-pi_h_u;
trial u (Wh); test v (Wh);
form m = integrate (u*v);
form a = integrate (dot(grad_s(u),grad_s(v)));
field one (Wh, 1);
Float meas_gamma = m(one,one);
Float lambda_e = m(one,eh)/meas_gamma;
eh = eh - lambda_e*one;
Float err_l2 = sqrt(m(eh,eh))/meas_gamma;
Float err_h1 = sqrt(a(eh,eh))/meas_gamma;
Float err_linf = eh.max_abs();
derr << "lambda_e = " << lambda_e << endl;
derr << "err_l2 = " << err_l2 << endl
<< "err_h1 = " << err_h1 << endl
<< "err_linf = " << err_linf << endl;
return (err_linf < tol) ? 0 : 1;
}
form
see the form page for the full documentation
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
main
int main(int argc, char **argv)
Definition: laplace_s_error.cc:25
field
see the field page for the full documentation
rheolef::integrate
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
space
see the space page for the full documentation
rheolef.h
rheolef - reference manual
a
Definition: diffusion_isotropic.h:25
rheolef::interpolate
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
eh
field_basic< T, M > eh
Definition: form_field_expr.h:58
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::grad_s
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
Definition: field_expr_terminal.h:929
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
test
see the test page for the full documentation
u
Definition: leveque.h:25
u_exact
g u_exact
Definition: taylor_exact.h:26
rheolef::derr
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
Float
see the Float page for the full documentation
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.a
a
Definition: mkgeo_ball.sh:151
trial
see the test page for the full documentation
torus.icc
The torus benchmark – level set, right-hand-side and exact solution.
rheolef::std
Definition: vec_expr_v2.h:391