> [...]
> It works in the serial case. However, it doesn't work when I use multiple 
> MPI processes. For my actual mesh, it breaks when n_processes >= 5. 
> Basically I have to make sure that dof 41 is included in the relevant dofs 
> of all the processes. How to I do that? I think this type of constraint is 
> different than a periodic boundary condition and I could not find a 
> dedicated function that takes care of it.
>
No, there is no function for that. It would of course be pretty simple if 
you just knew the value all these dofsshould be set to, but I assume that's 
not the case.

I didn't mean to say that you have to modify the locally relevant dofs, 
i.e. the IndexSet you obtain from DoFtools::locally_relevant_dofs, but tha 
tyou need to use an extended IndexSet in all the places you would normally 
use that IndexSet.
There is IndexSet::add_index that you can use to add entries to an existing 
IndexSet object.

Best,
Daniel

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