On Sun, 2 Apr 2006, Steffen Petersen wrote:
> This seems to be a bug in the 3D hierarchic shapes (and I just got poor
> results from a convergence test for the HEX27 hierarchics).
> It seems that no one has really used the 3D hierarchics so far.
I was afraid of that. I used the 3D hierarchics once when trying to
debug the 3D Hermites, and they didn't work... but I discovered a bug
in my user-level code, and after the Hermites started working I just
assumed the same bug had been responsible for the weird hierarchics
Ben expressed worry those long index lookup tables in
fe_hierarchic_shape_3D.C might be wrong. Well, the lookup tables are
just fine, but it looks like the real complication of the function is
in those long lists of orientation changes. I'd like to implement
arbitrary polynomial order for the 3D Hierarchics, and I can do most
of the work easily, but I'd been hoping to just copy the
orientation-matching code from the current cubic implementation.
> For the 3D Berstein shapes I had adopted the finite differences
> scheme that was used in libMesh to compute the shape derivatives for
> triangular elements. For the moderate orders that had been implemented
> so far this appears to work fine, but I guess it has limitations
> when used with high polynimial orders.
Everything has limitations when used with high polynomial orders; my
new 2D Hierarchic quads use the analytic derivatives, but they still
seem to become useless quickly for p>10. I ought to try recompiling
with long double support again, just to see how much farther they get
with a few digits extra precision.