Dear all,
I have a triangulation which has been refined along some (polygonal) patch, 
thus forming two non-overlapping domains (say, domain #1 and #2). My task 
is to extract cells for domain #1, and solve BVP for this domain (with 
known boundary conditions). The rest of the cells (domain #2) are not 
needed. An example of such situation is shown attached (with land and 
ocean/sea being two domains).

FWIW, the problem is posed in dim = 2, spacedim = 3. The solution is in H1. 

Here is what I struggle with:

- I thought of using 
GridGenerator::create_triangulation_with_removed_cells, but this one does 
not accept refined non-conforming meshes. 

- My next thought was to detect those edges, which domains #1 and #2 share 
and calculate face integrals on them during assembly, thus incorporating 
BCs. Will DoFTools::make_flux_sparsity_pattern be the right function for 
this? 

- Next, what should I do on cells in domain #2? Logically, I should somehow 
treat them with FE_Nothing... But how to get this done right?

Thanks! 

Alexander

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