Can one assume that the order that the (active) cells are traversed over in a loop such as:

    for (Triangulation<deal_II_dimension>::active_cell_iterator cell  = 
tri.begin_active() ;
cell != tri.end(); ++cell) is the always the same if the mesh has not been altered? I'm guessing not but hoping so.
Yes, you can. While you cannot rely on a specific ordering, the order will not change for a particular mesh. This is actually being used inside the library, where data of a mesh cell is stored in different vectors.

Best,
Guido
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