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

The Poisson problem by the hybrid discontinuous Galerkin method – post-treatment with the Raviart-Thomas element.

The Poisson problem by the hybrid discontinuous Galerkin method – post-treatment with the Raviart-Thomas element

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
field sigma_h, uh, lambda_h;
din >> catchmark("n") >> n
>> catchmark("beta") >> beta
>> catchmark("u") >> uh
>> catchmark("lambda") >> lambda_h
>> catchmark("sigma") >> sigma_h;
const geo& omega = uh.get_geo();
size_t d = omega.dimension();
size_t k = uh.get_space().degree();
string approx = (k == 0) ? "empty" : "P"+to_string(k-1)+"d";
space Tht(omega, "RT"+to_string(k)+"d");
space Wht(omega, approx, "vector");
space Mht(omega, "trace_n(RT"+to_string(k)+"d)");
space Sht = Wht*Mht;
trial sigma_t (Tht); test tau (Sht);
auto tau_internal = tau[0], tau_n = tau[1];
auto coef = beta*pow(h_local(),n);
form aht = integrate (dot(sigma_t, tau_internal)
+ on_local_sides (dot(sigma_t,normal())*tau_n));
field lht = integrate(dot(sigma_h, tau_internal)
+ on_local_sides((dot(sigma_h,normal())
+ coef*(lambda_h - uh))*tau_n));
field sigma_ht (Tht);
problem p (aht);
p.solve (lht, sigma_ht);
dout << catchmark("n") << n << endl
<< catchmark("beta") << beta << endl
<< catchmark("u") << uh
<< catchmark("lambda") << lambda_h
<< catchmark("sigma") << sigma_h
<< catchmark("sigmat") << sigma_ht;
}
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 space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
int main(int argc, char **argv)
rheolef::details::is_vec dot
This file is part of Rheolef.
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: 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:211
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value, details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
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
Float beta[][pmax+1]
STL namespace.
rheolef - reference manual
Definition: sphere.icc:25