Jump boundary condition (discontinous galerkin)

General Discussion
1

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

2

Yes some year ago, I Mc Bain exactly this problem in freefem day 2012

I have do a exemple but it is not clean .

1 Like
3

Thank you very much, dear professor.

In order to understand, why intalledges(Th)(…) or intallBE(Th)(…)
doesn’t work if i’m using galerkin discontinous?

4

If you use DG , it is a other story, it possible but I have no time to explain.