[petsc-dev] access to finite element second derivatives

[Matthew Knepley]

On Mon, Dec 2, 2013 at 4:49 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
> > So these elements are C1? I would have a tendency to fall back on mixed
> > formulations or interior penalty (I don't understand these) formulations
> for
> > this. Then C0 elements are alright.
>
> C^1 elements can be delicate beasts, though they wouldn't be hard to
> express now.  Second derivatives would be useful even for C^0 elements,
> to evaluate some error estimators and to provide stabilization terms
> like SUPG (with high-order elements).
>
> I have always disliked having separate tiny functions for each of the
> entries.  Once you add second derivatives, it is painfully obvious that
> humans will not be coding all those tiny functions, at which point it is
> clearly not the right interface.
>

I do not find this argument convincing, and I don't think its coherent
above.
Are you proposing to merge f0/f1/f2? That seems untenable since we must
test against different things, unless you want one fat functions with
f0/f1/f2
as arguments. That does not seem any simpler to me. If you mean you do not
want separate functions by field, I also do not agree. The indexing between
fields can get very ugly inside, and we have no good user support for that.

  Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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