So here's an embarrassing question from me:

Does libMesh not calculate dphi and d2phi properly for
lower-dimensional elements embedded at odd angles in
higher-dimensional spaces?

I always assumed that worked (despite having edited the code
myself...), and I even vaguely recall telling someone else that it
probably worked, but until now I've only solved zeroth-order systems
on BoundaryMeshes.  Now I'm trying a simple poisson type problem, and
I'm noticing that FEBase::compute_shape_functions() doesn't seem to be
at all designed for the case where a 1D element lives in 2D space or a
2D element lives in 3D space.  fe_base.C:708 could be calculating
dphi = infinity for an edge in the yz plane!

We seem to be doing everything correctly in compute_map(): dxidy_map
and dxidz_map get calculated for 1D elements, for example... so is
there any reason why we're not using these terms to do things right in
cases where they're non-zero?


Unless there's something I'm missing, I'd like to implement the
correct dphi/d2phi calculations in compute_shape_functions.

They are extra usually-unnecessary computations in 1D and 2D problems,
so anyone objects for efficiency reasons scream now.  My personal
philosophy is a mix of "lower-dimensional problems are usually cheap
to begin with" and "if you want them cheaper you can always use a
--enable-2D-only or --enable-1D-only configure", but I'm open to being
reasoned with.  ;-)
---
Roy

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