Erik,

you might want to have a look at
https://groups.google.com/d/msg/dealii/wG6aJdXHweA/IcsUjxj5dFsJ

Basically, I would loop through all the neighbors recursively only 
considering cells that have a vertex with the face you are looking for in 
common.
You can access the DoFs on faces just as for cells via 

std::vector<types::global_dof_index> dof_indices(fe.dofs_per_face);
for (; cell != endc; ++cell)
      if (!cell->is_artificial())
        for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; 
++face)
          [...]
          cell->face(face)->get_dof_indices(dof_indices);
          [...]

Maybe also look into step-42 for accessing DoFs on faces.

Best,
Daniel

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