Daniel,

DoFTools::dof_indices_with_subdomain_association returns the degrees of 
> freedom of all the cells that have the given subdomain id. For 
> parallel::distributed::Triangulation objects the subdomain id is the the 
> MPI rank and this is the only valid input.
> In this case, the function simply returns all the degrees of freedom on 
> locally owned cells. If a finite element defines degrees of freedoms that 
> are associated with a face, these degrees of freedom are part of all the 
> IndexSet objects in case the face is located on the interface between two 
> subdomains. For a parallel::distributed::Triangulation object, these are 
> the degrees of freedom on the faces to ghosted cells


Thanks for the reply. Indeed the indices given by 
DoFHandler::locally_owned_dofs() and 
DoFTools::dof_indices_with_subdomain_association() are identical for FE_DGQ 
element. I have checked this in my code.

You could still ask for the unit support points and figure out which of 
> them are geometrically on a given face.


This is definitely possible, but would probably be inefficient if I code 
for it. Isn't there a function in DoFTools which does this? Because not 
marking all dofs of ghost cells as relevant will give much savings in 
communication, I was wondering if DoFTools already doesn't have an 
implementation for this.

However, note that as soon as gradients are involved all the degrees of 
> freedom contribute to values on faces.


I don't have much experience in parallel programming, but I think we can 
circumvent this by computing gradients at all dof locations in a subdomain 
and again only communicating data of dofs lying on subdomain interfaces. I 
might need some correction on this :).

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