[Getfem-users] Tests with functions which satisfies homogeneous Dirichlet boundary conditions

[Yassine ZAIM]

Hello everyone,

I want know if some one has been trying already to change the exact solution, and the second member to a polynomes. I want make a test with a function which satisfies the homogeneous Dirichlet boundary conditions. 

So for exemple, for the Laplacian problem, N=2 dimensions, I make :

/* exact solution */

scalar_type sol_u(const base_node &x) { return (pow(x[0],2) - pow(x[0],1))*pow(x[1],1); }

/* righ hand side */

scalar_type sol_f(const base_node &x)

{ return 2*pow(x[1],1); }

/* gradient of the exact solution */

base_small_vector sol_grad(const base_node &x)

{ base_small_vector res(2);

res[0] = (2*pow(x[0],1) - 1)*pow(x[1],1);

res[1] = pow(x[0],2) - pow(x[0],1);

return res; }

But with these functions I can't find the good result, and the good order of convergence, I found the error : 

L2 error = 0.1676465135960112

H1 error = 0.6176167218760237

Linfty error = 0.3381665840490764

The same problem for the elastostatic problem also.

Thank you, in advance for your help.

 ​

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ZAIM Yassine 

PhD Student in Applied Mathematics