Rheolef  7.2
an efficient C++ finite element environment
p_laplacian_error.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 #include "p_laplacian_circle.h"
29 int main(int argc, char**argv) {
30  environment rheolef (argc,argv);
31  Float tol = (argc > 1) ? atof(argv[1]) : 1e-15;
32  Float p;
33  field uh;
34  din >> catchmark("p") >> p
35  >> catchmark("u") >> uh;
36  const geo& omega = uh.get_geo();
37  const space& Xh = uh.get_space();
38  field pi_h_u = lazy_interpolate (Xh, u_exact(p));
39  field eh = pi_h_u - uh;
40  integrate_option iopt;
42  iopt.set_order(2*Xh.degree());
43  Float err_lp = pow(integrate (omega,
44  pow(fabs(uh - u_exact(p)), p), iopt), 1./p);
45  Float err_w1p = pow(integrate (omega,
46  pow(norm(grad(uh) - grad_u(p)), p), iopt), 1./p);
47  Float err_linf = eh.max_abs();
48  dout << "err_linf = " << err_linf << endl
49  << "err_lp = " << err_lp << endl
50  << "err_w1p = " << err_w1p << endl;
51  return (err_linf < tol) ? 0 : 1;
52 }
see the Float page for the full documentation
see the field page for the full documentation
see the geo page for the full documentation
see the catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:121
see the integrate_option page for the full documentation
void set_family(family_type type)
idiststream din(cin)
see the diststream page for the full documentation
Definition: diststream.h:464
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:467
see the space page for the full documentation
This file is part of Rheolef.
std::enable_if< details::has_field_rdof_interface< 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
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
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition: vec.h:387
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
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
The p-Laplacian problem on a circular geometry – exact solution.
int main(int argc, char **argv)
rheolef - reference manual
Definition: sphere.icc:25
g u_exact
Definition: taylor_exact.h:26