### Discontinuous mesh-conforming interpolations in the interior

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10 weeks ago by
Hi,

I am looking for general directions for a problem that we are trying to solve with fenics. We have two sub-domains $\Omega_1$ and $\Omega_2$ and their interface, $\Gamma$. I am trying to solve this problem with interpolations that are continuous and $H^1$ in the interior of $\Omega_1$ and $\Omega_2$, and discontinuous across $\Gamma$. The formulation has integrals on $Omega_1$, $\Omega_2$ and $\Gamma$. On $\Gamma$ the integrals have jumps in weighting functions/trial solution and jumps in their normal derivatives.

Is there a preferred way to solve this? Digging through old Q&As I found that using two copies of dof's and setting one set to zero on either side of the interface through DirichletBC is a way to go. Is there a better option?

Thanks,