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cosinusprod_post_dg.cc
Go to the documentation of this file.
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "cosinusprod.h"
#include "cosinusprod_grad.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"+to_string(k));
Vh.block("boundary");
space Wh (omega["boundary"], "P"+to_string(k));
test u (Vh); trial v (Vh);
integrate_option fopt;
fopt.lump = true;
fopt.set_family(integrate_option::gauss_lobatto);
fopt.set_order(k);
form m = integrate (u*v, fopt);
field lh = integrate (uh*v, fopt);
field uh_star (Vh, 0);
uh_star ["boundary"] = lazy_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"+to_string(k+1)+"d");
field eh = lazy_interpolate (Xh1, uh-u_exact(d));
field eh_star = lazy_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 = lazy_interpolate (G0h, grad_h(eh));
field grad_eta_h = lazy_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 = lazy_interpolate (X0h, sqrt(s_eta_h2));
field s_eh2 = integrate (sqr(uh-u_exact(d))*v0);
field s_eh = lazy_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
;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition integrate_option.h:125
rheolef::integrate_option::lump
bool lump
Definition integrate_option.h:168
rheolef::integrate_option::gauss_lobatto
@ gauss_lobatto
Definition integrate_option.h:133
rheolef::integrate_option::gauss
@ gauss
Definition integrate_option.h:132
rheolef::integrate_option::set_family
void set_family(family_type type)
Definition integrate_option.h:260
rheolef::integrate_option::set_order
void set_order(size_t r)
Definition integrate_option.h:254
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
cosinusprod.h
The cosinus product function.
cosinusprod_grad.h
The cosinus product function – its gradient.
main
int main()
Definition field2bb.cc:58
Xh1
space_basic< T, M > Xh1
Definition field_expr.h:232
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::grad
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad(const Expr &expr)
grad(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:930
rheolef::lazy_interpolate
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::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition vec.h:379
rheolef::grad_h
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:968
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:211
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
grad_u
Definition combustion_exact.icc:34
u_exact
Definition interpolate_RTk_polynom.icc:125
u
Definition leveque.h:25