Hello FEniCS community,

I am trying to solve the advection-diffusion equation, but the Newton solver is currently not converging from maximum iterations being reached. This occurs when I define a Neumann source on an internal boundary. A solution is found when the Neumann condition is placed on an external boundary, so I don’t think the problem is ill-posed.

The interior boundary source is shown as the last term in the following weak form:

```
F = ((u_1 - u_n1) / k)*v_1*dx + dot(w, grad(u_1))*v_1*dx \
+ D*dot(grad(u_1), grad(v_1))*dx + flux*v_1('-')*dS(1)
```

It may be worth noting that I have a single Dirichlet condition defined on an exterior boundary, I’ve confirmed that the facets are properly labeled, I’ve redefined the measure of integration for interior facets, and that the interior facets of interest are on the boundary.

Any thoughts would be appreciated!