Hi everyone,

I would like to implement the following variational problem:

\begin{cases} -div(A_i \nabla u_i) = f \text{ in } \Omega_i \\ (A_1 \nabla u_1) \cdot n = (A_2 \nabla u_2) \cdot n \text{ on } \Gamma = \partial \Omega_1 \cap \partial \Omega_2 \\ (A_1 \nabla u_1) \cdot n = \alpha(u_2 - u_1) = \alpha[u] \text{ on } \Gamma = \partial \Omega_1 \cap \partial \Omega_2 \\ Ai \nabla u_i = 0 \text{ on } \Gamma_N \\ u = g_D \text{ on } \Gamma_D \end{cases}

The variational formulation is in a broken sobolev space (due to the discontinuity at \Gamma):

\int_{\Omega_1}A_1 \nabla u_1 \cdot \nabla v_1 dx + \int_{\Omega_2}A_2 \nabla u_2 \cdot \nabla v_2 dx + \int_\Gamma \alpha [u][v] ds = 0

with u=g_D \text{ on } \Gamma_D

Is it possible to to this in FreeFEM? in particular for the jump on the boundary condition at the interface \Gamma. I know that in FreeFEM it exists the discontinuous galerkin, but when i tried to do this, it says me the following error:

Error umpfack umfpack_di_numeric status 1

Error umfpack_di_solve status 1

Merci bcp,

Rodrigo