Solve Poisson equation with non-linear boundary conditions on a submesh

This code is way to big for me to review it. Make a minimal example following Read before posting: How do I get my question answered?

If you have issues with marking the unstructured meshes, i would suggest using Gmsh and the BooleanFragments operator to make sure that the interface between the two domains is resolved. To load gmsh meshes into dolfin, you can use for instance: Converter from GMSH to XDMF (with physical groups). There are many examples on how to use gmsh in this thread Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio (this post might be of special interest as it uses boolean fragments)

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