Multi-physics problems with different discrete models

Hi all,

We would like to solve multi-physics problems with variables defined in different discrete models and, possibly, coupled through Lagrange multiplier (either ConstantFESpace or FESpace on lower-dimensional grid). This is currently not supported in Gridap since all the spaces in a MultifieldFESpace have to share the same background DiscreteModel. Has someone done any work related to this? Would that be something worth exploring?

@santiagobadia, @JordiManyer

Start by reviewing MultifieldFESpace and the current requirement that its spaces share one background DiscreteModel; no files or tests are named in the issue. Define the design needed for different discrete models and lower-dimensional Lagrange-multiplier spaces, then add coverage showing coupled multiphysics spaces work across those models.

Written by the indexing model from the issue text.