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Hi Kaushik,
Yes, this is possible by changing a cell from FE_Nothing to FE_Q using p-refinement.
You can do this with the method described in #11132: Imitate what p::d::SolutionTransfer is doing with the more versatile tool p::d::CellDataTransfer and consider the following:
This leaves you with a correctly interpolated solution on the new mesh, where all newly activated dofs have the value `infinity`.
You can now (and not earlier!!!) assign the values you have in mind
for the newly activated dofs. You may want to exchange data on ghost
cells once more with `GridTools::exchange_cell_data_to_ghosts()`.
This is a fairly new feature in the library for a very specific use
case, so there is no dedicated class for transferring solutions across
finite element activation yet. If you successfully manage to make this
work, would you be willing to turn this into a class for the deal.II
library?
Marc
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