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p_laplacian_error.cc
Go to the documentation of this file.
#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::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
grad_u
tensor grad_u
Definition diffusion_transport_tensor_exact.icc:26
main
int main()
Definition field2bb.cc:58
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::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition space_mult.h:120
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::norm
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition vec.h:387
std
STL namespace.
p_laplacian_circle.h
The p-Laplacian problem on a circular geometry – exact solution.
rheolef.h
rheolef - reference manual
p
Definition sphere.icc:25
u_exact
g u_exact
Definition taylor_exact.h:26