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

The elasticity problem with the Taylor benchmark and discontinuous Galerkin method – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "taylor_exact.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
Float err_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
bool dump = (argc > 2);
field uh; din >> uh;
space Xh = uh.get_space();
geo omega = Xh.get_geo();
size_t k = Xh.degree();
size_t d = omega.dimension();
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*k+1);
string high_approx = "P"+itos(k+1)+"d";
space Xh1 (omega, high_approx, "vector"),
Qh1 (omega, high_approx);
field eh = interpolate (Xh1, uh-u_exact());
Float err_l2 = sqrt(integrate (omega, norm2(uh-u_exact()), iopt));
Float err_linf = eh.max_abs();
Float err_h1 = sqrt(integrate (omega, norm2(grad_h(eh)), iopt)
+ integrate (omega.sides(), (1/h_local())*norm2(jump(eh)), iopt));
derr << "err_l2 = " << err_l2 << endl
<< "err_linf = " << err_linf << endl
<< "err_h1 = " << err_h1 << endl;
if (dump) {
dout << catchmark("uh") << uh
<< catchmark("u") << interpolate (Xh, u_exact())
<< catchmark("eu") << eh;
}
return (err_linf <= err_linf_expected) ? 0 : 1;
}
see the Float page for the full documentation
see the field page for the full documentation
see the geo 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
int main(int argc, char **argv)
field_basic< T, M > eh
verbose clean transpose logscale grid shrink ball stereo iso volume skipvtk deformation fastfieldload lattice reader_on_stdin color format format format format format format format format format format format format format format format format format format dump
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
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
The Taylor benchmark – the exact solution of the Stokes problem.
g u_exact
Definition: taylor_exact.h:26