This is the scilab/demos/demo_laplacian.sce example.
gf_workspace('clear all'); m = gf_mesh('cartesian',[0:.1:1],[0:.1:1]); // create a mesh_fem of for a field of dimension 1 (i.e. a scalar field) mf = gf_mesh_fem(m,1); // assign the Q2 fem to all convexes of the mesh_fem, gf_mesh_fem_set(mf,'fem',gf_fem('FEM_QK(2,2)')); // an exact integration will be used mim = gf_mesh_im(m, gf_integ('IM_GAUSS_PARALLELEPIPED(2,10)')); // detect the border of the mesh border = gf_mesh_get(m,'outer faces'); // mark it as boundary #1 gf_mesh_set(m, 'boundary', 1, border); gf_plot_mesh(m, 'regions', [1]); // the boundary edges appears in red // interpolate the exact solution Uexact = gf_mesh_fem_get_eval(mf, list('y.*(y-1).*x.*(x-1)+x.^5')); // its second derivative F = gf_mesh_fem_get_eval(mf, list('-(2*(x.^2+y.^2)-2*x-2*y+20*x.^3)')); md=gf_model('real'); gf_model_set(md, 'add fem variable', 'u', mf); gf_model_set(md, 'add Laplacian brick', mim, 'u'); gf_model_set(md, 'add initialized fem data', 'VolumicData', mf, F); gf_model_set(md, 'add source term brick', mim, 'u', 'VolumicData'); gf_model_set(md, 'add initialized fem data', 'DirichletData', mf, Uexact); gf_model_set(md, 'add Dirichlet condition with multipliers', mim, 'u', mf, 1, 'DirichletData'); gf_model_get(md, 'solve'); U = gf_model_get(md, 'variable', 'u'); printf('H1 norm of error: %g\n', gf_compute(mf,U-Uexact,'H1 norm',mim)); subplot(2,1,1); gf_plot(mf,U,'mesh','on','contour',.01:.01:.1); colorbar(min(U),max(U)); title('computed solution'); subplot(2,1,2); gf_plot(mf,U-Uexact,'mesh','on'); colorbar(min(U-Uexact),max(U-Uexact)); title('difference with exact solution'); | ![]() | ![]() |
Y. Collette