Rheolef  7.2
an efficient C++ finite element environment
laplace_s_error.cc
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1 #include "rheolef.h"
22 using namespace rheolef;
23 using namespace std;
24 #include "torus.icc"
25 int main (int argc, char**argv) {
26  environment rheolef (argc, argv);
27  Float tol = (argc > 1) ? atof(argv[1]) : 1e-7;
28  field uh;
29  din >> uh;
30  const space& Wh = uh.get_space();
31  field pi_h_u = lazy_interpolate(Wh, u_exact());
32  field eh = uh-pi_h_u;
33  trial u (Wh); test v (Wh);
34  form m = integrate (u*v);
35  form a = integrate (dot(grad_s(u),grad_s(v)));
36  field one (Wh, 1);
37  Float meas_gamma = m(one,one);
38  Float lambda_e = m(one,eh)/meas_gamma;
39  eh = eh - lambda_e*one;
40  Float err_l2 = sqrt(m(eh,eh))/meas_gamma;
41  Float err_h1 = sqrt(a(eh,eh))/meas_gamma;
42  Float err_linf = eh.max_abs();
43  derr << "lambda_e = " << lambda_e << endl;
44  derr << "err_l2 = " << err_l2 << endl
45  << "err_h1 = " << err_h1 << endl
46  << "err_linf = " << err_linf << endl;
47  return (err_linf < tol) ? 0 : 1;
48 }
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 environment page for the full documentation
Definition: environment.h:121
idiststream din(cin)
see the diststream page for the full documentation
Definition: diststream.h:464
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:473
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
point u(const point &x)
int main(int argc, char **argv)
This file is part of Rheolef.
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
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
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
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_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
rheolef - reference manual
Definition: leveque.h:25
g u_exact
Definition: taylor_exact.h:26
The torus benchmark – level set, right-hand-side and exact solution.