p_laplacian_error.cc
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#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 = 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;
}
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::integrate_option::set_order
void set_order(size_t r)
Definition: integrate_option.h:254
field
see the field page for the full documentation
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:202
p_laplacian_circle.h
The p-Laplacian problem on a circular geometry – exact solution.
space
see the space page for the full documentation
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
rheolef::grad
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
Definition: field_expr_terminal.h:911
rheolef::norm
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition: vec.h:387
rheolef.h
rheolef - reference manual
main
int main(int argc, char **argv)
Definition: p_laplacian_error.cc:29
p
Definition: sphere.icc:25
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
rheolef::integrate_option::gauss
@ gauss
Definition: integrate_option.h:132
rheolef::interpolate
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
eh
field_basic< T, M > eh
Definition: form_field_expr.h:58
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
u_exact
g u_exact
Definition: taylor_exact.h:26
Float
see the Float page for the full documentation
grad_u
tensor grad_u
Definition: transport_tensor_exact.icc:26
rheolef::integrate_option::set_family
void set_family(family_type type)
Definition: integrate_option.h:260
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::std
Definition: vec_expr_v2.h:391
geo
see the geo page for the full documentation