Hi All,
I'm submitting a patch with improvements and bug fixes for XYZ basis functions.
I haven't been able to test it against the svn head because I had compilation
issues. See the error file.
However, since the patch is only related to fe_xyz*.C, it should work.
The major change is related to a scaling introduced to improve the condition
number on small and big elements (small and big compared to the reference
element).
With such a scaling on linear hexs the XYZ is equivalent to a MONOMIAL basis,
independently of the element size.
On curved elements the approximation properties of this scaled XYZ should be
better than MONOMIAL and should allow to go up to a third or fourth degree
approximation without any trouble.
Another step would be to introduce a rotation in order to define the XYZ basis
using a frame oriented with the principal axis of inertia of the mesh element.
This might help on stretched elements.
I hope that the patch will be included in future libMesh releases.
Thanks
Lorenzo
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