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///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2018 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
///
/// =========================================================================
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "contraction.h"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space X1h = contraction::velocity_space (omega, "P1");
space Bh (omega, "bubble", "vector");
space Xh = X1h * Bh;
space Qh (omega, "P1");
trial u1 (X1h), ub (Bh), p (Qh);
test v1 (X1h), vb (Bh), q (Qh);
form a1 = integrate (2*ddot(D(u1),D(v1)));
form ab = integrate (2*ddot(D(ub),D(vb)));
form b1 = integrate (-div(u1)*q);
form bb = integrate (-div(ub)*q);
form a = {{a1, 0},
{ 0, ab}};
form b = {b1, bb};
a.set_uu().set_symmetry(true);
field uh (Xh, 0), ph (Qh, 0);
uh[0] = contraction::velocity_field (X1h);
problem_mixed stokes (a, b);
stokes.solve (field(Xh,0), field(Qh,0), uh, ph);
dout << catchmark("inv_lambda") << 0 << endl
<< catchmark("u") << uh[0]
<< catchmark("ub") << uh[1]
<< catchmark("p") << ph;
}
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