I have 3D DG-elliptic solver and it performs integration over the faces of
interior sides of elements.  Without AMR this is not a problem because I can
initialize a FE object for any given side of an element.  However, with AMR,
I run into a problem.  When one element is coarser than its neighbor then,
from the perspective of the coarser element, I need to perform integration
over a subregion of a given side.  Is there some convenient method to
initialize a FE object for this sub-region? Or, is the best I can do to
extract the quadrature points from an FE object initialized for the finer
element and remap then into the space of the larger?

I recoginize that this shouldn't be too hard, but I was hoping to learn
something about libmesh and I wanted to make sure that there were no subtle
points about FE initialization I was missing.

Thanks

Adam
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