Hi Praveen,
no, MappingQ does not unless you set the second boolean flag in the
constructor to enable the mapping on all cells and not just the
boundary. Even worse, when you have attached a curved manifold on the
cells and not just the boundary you will have gaps in your computational
domain. I highly recommend using MappingQGeneric instead.
Best,
Martin
P.S. We had a discussion about removing the class MappingQ and just use
MappingQGeneric always just the other day:
https://github.com/dealii/dealii/issues/3874#issuecomment-305513405 (and
subsequent comments).