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///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//! @examplefile convect_error.cc Convection-diffusion equation by the method of characteristics -- error analysis
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "rotating-hill.h"
int main (int argc, char **argv) {
environment rheolef (argc,argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-10;
Float nu;
din >> catchmark("nu") >> nu;
branch get ("t","phi");
branch put ("t","phi_h","pi_h_phi");
derr << "# t\terror_l2\terror_linf" << endl;
field phi_h;
Float err_l2_l2 = 0;
Float err_linf_linf = 0;
for (Float t = 0, t_prec = 0; din >> get (t, phi_h); t_prec = t) {
const space& Xh = phi_h.get_space();
size_t d = Xh.get_geo().dimension();
field pi_h_phi = lazy_interpolate (Xh, phi(d,nu,t));
trial phi (Xh); test psi (Xh);
form m = integrate (phi*psi);
field eh = phi_h - pi_h_phi;
Float err_l2 = sqrt(m(eh,eh));
Float err_linf = eh.max_abs();
err_l2_l2 += sqr(err_l2)*(t - t_prec);
err_linf_linf = max(err_linf_linf, err_linf);
dout << put (t, phi_h, pi_h_phi);
derr << t << "\t" << err_l2 << "\t" << err_linf << endl;
}
derr << "# error_l2_l2 = " << sqrt(err_l2_l2) << endl;
derr << "# error_linf_linf = " << err_linf_linf << endl;
return (err_linf_linf <= tol) ? 0 : 1;
}
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