Rheolef  7.2
an efficient C++ finite element environment
sinusprod_error_hdg.cc
Go to the documentation of this file.
1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "sinusprod.h"
29 #include "sinusprod_grad.h"
30 int main(int argc, char**argv) {
31  environment rheolef(argc, argv);
32  Float err_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
33  bool with_u = (argc <= 2) || argv[2] != string("-us");
34  bool with_sigma = ((argc <= 2) || argv[2] != string("-no-sigma")) && with_u;
35  field uh, lambda_h, sigma_h;
36  if (with_u) {
37  din >> catchmark("u") >> uh; // hdg or hho
38  } else {
39  din >> catchmark("us") >> uh; // hho
40  }
41  din >> catchmark("lambda") >> lambda_h;
42  if (with_sigma) {
43  din >> catchmark("sigma") >> sigma_h;
44  }
45  space Xh = uh.get_space();
46  geo omega = Xh.get_geo();
47  size_t k = Xh.degree();
48  size_t d = omega.dimension();
49  integrate_option iopt;
51  iopt.set_order(3*(k+1)+4);
52  Float err_u_l2 = sqrt(integrate (omega, sqr(uh-u_exact(d)), iopt));
53  string opts = Xh.get_basis().option().stamp();
54  space Xh1 (omega, "P"+to_string(k+1)+"d"+opts);
55  field euh = lazy_interpolate (Xh1, uh-u_exact(d));
56  Float err_u_linf = euh.max_abs();
57  Float err_u_h1 = sqrt(integrate (omega, norm2(grad_h(euh)), iopt)
58  + integrate (omega.sides(), (1/h_local())*sqr(jump(euh)), iopt));
59  derr << "err_u_l2 = " << err_u_l2 << endl
60  << "err_u_linf = " << err_u_linf << endl
61  << "err_u_h1 = " << err_u_h1 << endl;
62  if (with_sigma) {
63  Float err_sigma_l2 = sqrt(integrate (omega, norm2(sigma_h-grad_u(d)), iopt));
64  space Th1 (omega, "P"+to_string(k+1)+"d"+opts, "vector");
65  field esh = lazy_interpolate (Th1, sigma_h-grad_u(d));
66  Float err_sigma_linf = esh.max_abs();
67  derr << "err_sigma_l2 = " << err_sigma_l2 << endl
68  << "err_sigma_linf = " << err_sigma_linf << endl;
69  }
70  if (!lambda_h.get_space().get_basis().option().is_trace_n()) {
71  space Mh = lambda_h.get_space();
72  trial lambda(Mh); test mu(Mh);
73  form ms = integrate(lambda*mu);
74  field kh = integrate(u_exact(d)*mu, iopt);
75  field ph_lambda(Mh);
76  problem pms (ms);
77  pms.solve (kh, ph_lambda);
78  Float err_lambda_l2 = sqrt(integrate (omega["sides"], h_local()*sqr(lambda_h-ph_lambda), iopt));
79  derr << "err_lambda_l2 = " << err_lambda_l2 << endl;
80  }
81  return (err_u_linf <= err_linf_expected) ? 0 : 1;
82 }
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 geo page for the full documentation
see the problem page for the full documentation
see the catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:121
see the integrate_option page for the full documentation
void set_family(family_type type)
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
space_basic< T, M > Xh1
Definition: field_expr.h:232
This file is part of Rheolef.
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: 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
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_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef - reference manual
The sinus product function.
int main(int argc, char **argv)
The sinus product function – its gradient.
g u_exact
Definition: taylor_exact.h:26