Coupling of two submeshes using constraints

[paul-hilscher]

Dear MFEM Team,

I am looking to couple two submeshes and I was hoping you could provide some guidance or share an example with me.

The equation I'm trying to solve is $\textrm{div} \vec{j} = 0$ (the electric current conduction equation) given by:
$$\nabla \cdot \sigma \nabla \phi = 0 \quad,$$
where $\phi$ is the electric potential and $\sigma$ is the electrical conductivity.

For the geometry, let's assume that I have two adjacent cubes with attributes A and B, from which I create two submeshes (note that I have just started learning about submeshes so I might have still the wrong idea about them)

   _________ _________
  |         |         |
  |    A    |    B    |
  |_________|_________|

            | Create submeshes
       	    v
 _________     _________
|         |   |         |
|    A    |   |    B    |
|_________|   |_________|

1. Now I would like to use homogeneous constraints to couple both submeshes together into the same equation system. Essentially the true dofs would be the same as on the original mesh. How can this be achieved ?

2. For modelling a plasma sheet or an electrical double layer I would like to use a non-homogeneous constraint (voltage drop) instead. How can this be done ?

Many thanks !