Hi Doug,

when dealing with distributed meshes, ownership of cells change and we may 
not know which finite element lives on cells that the process got recently 
assigned to. Thus, we need to transfer each cell's `active_fe_index`, which 
we do automatically during coarsening and refinement. However, you set 
`active_fe_indices` after refinement happened, which works in the serial 
case, but no longer in the parallel one. Before executing refinement, you 
need to set `future_fe_indices` that describe to which finite element your 
cell will be assigned to, and you need to do that before refinement 
happened! This should resolve both issues.

Further, you initialize `LinearAlgebra::distrtibuted::Vector` objects 
without any parallel distribution by using this constructor. 
<https://www.dealii.org/current/doxygen/deal.II/classLinearAlgebra_1_1distributed_1_1Vector.html#a3be6c4ce529bb9b6c13eb831d0a86f55>
 
Try using one a different one.

Please see `tests/mpi/solution_transfer_04.cc 
<https://github.com/dealii/dealii/blob/master/tests/mpi/solution_transfer_04.cc>`
 
and `tests/mpi/p_coarsening_and_refinement.cc 
<https://github.com/dealii/dealii/blob/master/tests/mpi/p_refinement_and_coarsening.cc>`
 
for working examples (I guess we should provide one using an actual 
`SolutionTransfer` object as well), that should hopefully be applicable to 
your problem. This is a recently added feature: If you have any suggestions 
for improvement or encounter more problems, feel free to message us!

Marc

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