I think I found the problem regarding the mesh refinement issue in parallel 
mode. Probably, it is not even related to the boundary indicators. From 
what I understood, there is a problem with the MPI_Allreduce function I 
mentioned in the previous post: 
https://groups.google.com/forum/#!topic/dealii/aDEP1MSS0JA. Hence, Daniel 
was totally right. I cite:

- *n_vertices() only gives you the number of vertices for one process, not 
> the global one.* In particular, you can't rely on the fact that this is 
> the same for all processes. Furthermore, you (probably) don't initialize 
> all the values of your struct. This might be the reason for the large 
> numbers you are observing.
>

I observed that my total number of nodes (* triangulation.n_vertices() *) 
and elements ( *triangulation.n_active_cells()* ) remain the same even 
after refinement, but the total number of degrees of freedom ( 
*dof_handler.n_dofs()* ) are updated. Is there a possibility to obtain the 
total number of nodes after refinement/coarsening or do I have to use the 
DoF information somehow?

Sorry for the confusion.

Best,
Seyed Ali 

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