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p_laplacian_error.cc

The p-Laplacian problem on a circular geometry – error analysis.

The p-Laplacian problem on a circular geometry – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "p_laplacian_circle.h"
int main(int argc, char**argv) {
environment rheolef (argc,argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-15;
Float p;
field uh;
din >> catchmark("p") >> p
>> catchmark("u") >> uh;
const geo& omega = uh.get_geo();
const space& Xh = uh.get_space();
field pi_h_u = lazy_interpolate (Xh, u_exact(p));
field eh = pi_h_u - uh;
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*Xh.degree());
Float err_lp = pow(integrate (omega,
pow(fabs(uh - u_exact(p)), p), iopt), 1./p);
Float err_w1p = pow(integrate (omega,
pow(norm(grad(uh) - grad_u(p)), p), iopt), 1./p);
Float err_linf = eh.max_abs();
dout << "err_linf = " << err_linf << endl
<< "err_lp = " << err_lp << endl
<< "err_w1p = " << err_w1p << endl;
return (err_linf < tol) ? 0 : 1;
}
Float
see the Float page for the full documentation
field
see the field page for the full documentation
geo
see the geo 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::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
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
std
STL namespace.
p_laplacian_circle.h
The p-Laplacian problem on a circular geometry – exact solution.
rheolef.h
rheolef - reference manual
grad_u
Definition combustion_exact.icc:34
p
Definition sphere.icc:25
u_exact
Definition interpolate_RTk_polynom.icc:125