Rheolef  7.1
an efficient C++ finite element environment
cosinusprod_post_dg.cc

The cosinus product function – post-treatment with the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "cosinusprod.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
field uh; din >> uh;
space Xh = uh.get_space();
geo omega = Xh.get_geo();
size_t k = Xh.degree();
size_t d = omega.dimension();
space Vh (omega, "P"+itos(k));
Vh.block("boundary");
space Wh (omega["boundary"], "P"+itos(k));
test u (Vh); trial v (Vh);
integrate_option fopt;
fopt.lump = true;
fopt.set_order(k);
form m = integrate (u*v, fopt);
field lh = integrate (uh*v, fopt);
field uh_star (Vh, 0);
uh_star ["boundary"] = interpolate(Wh, u_exact(d));
problem pm (m);
pm.solve (lh, uh_star);
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*k+1);
space Xh1 (omega, "P"+itos(k+1)+"d");
field eh_star = interpolate (Xh1, uh_star-u_exact(d));
field eta_h = eh_star - eh;
Float err_linf = eh.max_abs();
Float err_star_linf = eh_star.max_abs();
Float eta_linf = eta_h.max_abs();
Float err_l2 = sqrt(integrate (omega, sqr(uh-u_exact(d)), iopt));
Float err_star_l2 = sqrt(integrate (omega, sqr(uh_star-u_exact(d)), iopt));
Float eta_l2 = sqrt(integrate (omega, sqr(eta_h), iopt));
Float err_h1 = sqrt(integrate (omega, norm2(grad_h(uh)-grad_u(d)), iopt));
Float err_star_h1 = sqrt(integrate (omega, norm2(grad(uh_star)-grad_u(d)), iopt));
Float eta_h1 = sqrt(integrate (omega, norm2(grad_h(eta_h)), iopt));
// gradient as P0
space G0h (omega, "P0", "vector");
field grad_eh = interpolate (G0h, grad_h(eh));
field grad_eta_h = interpolate (G0h, grad_h(eta_h));
// proj gradient as P1
space G1h (omega, "P1", "vector");
G1h.block("boundary");
test uu (G1h); trial vv (G1h);
form m1v = integrate(dot(uu,vv), fopt);
field l1h = integrate (dot(grad_eh,vv));
field grad_eh_p1 (G1h, 0);
problem pm1v (m1v);
pm1v.solve(l1h, grad_eh_p1);
field l2h = integrate (dot(grad_eta_h,vv));
field grad_eta_h_p1 (G1h, 0);
pm1v.solve(l2h, grad_eta_h_p1);
// calcul de s_eta_h = sqrt(int_K eta_h^2 dx) : P0
space X0h (omega, "P0");
test v0 (X0h);
field s_eta_h2 = integrate (sqr(eta_h)*v0);
field s_eta_h = interpolate (X0h, sqrt(s_eta_h2));
field s_eh2 = integrate (sqr(uh-u_exact(d))*v0);
field s_eh = interpolate (X0h, sqrt(s_eh2));
derr << "err_l2 = " << err_l2 << endl
<< "eta_l2 = " << eta_l2 << endl
<< "err_star_l2 = " << err_star_l2 << endl
<< "err_linf = " << err_linf << endl
<< "eta_linf = " << eta_linf << endl
<< "err_star_linf = " << err_star_linf << endl
<< "err_h1 = " << err_h1 << endl
<< "eta_h1 = " << eta_h1 << endl
<< "err_star_h1 = " << err_star_h1 << endl;
dout << catchmark ("grad_eta_h") << grad_eta_h_p1
<< catchmark ("grad_eh") << grad_eh_p1
<< catchmark ("eta_h") << eta_h
<< catchmark ("eh") << eh
<< catchmark ("uh") << uh
<< catchmark ("uh_star") << uh_star
<< catchmark ("s_eta_h") << s_eta_h
<< catchmark ("s_eh") << s_eh
;
}
field lh(Float epsilon, Float t, const test &v)
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
T max_abs() const
Definition: field.h:731
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
The cosinus product function.
The cosinus product function – its gradient.
int main(int argc, char **argv)
space_basic< T, M > Xh1
Definition: field_expr.h:263
field_basic< T, M > eh
This file is part of Rheolef.
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_convertible< 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
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_h(const Expr &expr)
grad_h(uh): 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:202
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
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef - reference manual
Definition: leveque.h:25
g u_exact
Definition: taylor_exact.h:26
Float u(const point &x)
tensor grad_u