On Mon, 24 Jan 2011, Saurabh Srivastava wrote:
--- I'm using Hierarchic basis ...and I checked the second
derivatives for 1st order basis are between 1e-5 to 1e-11 at several
quadrature points which is though small but non-zero. Indeed on
your suggestion when I changed the basis to Lagrangian i got exact
zeros.
Yeah, grep through fe_hierarchic_shape_2D.C for "I have been lazy
here". I never needed second derivatives on hierarchic elements for
myself, but I didn't want to leave them completely unimplemented, so I
just tossed in a central differencing of the first derivatives. That
would still come out exactly zero for constant first derivatives, but
on your triangles those aren't perfectly constant, because in that
case the HIERARCHIC first derivatives are finite differenced too!
I'll Cc: this to the mailing lists, in case any altruistic folks want
to code up analytic derivative evaluations. Altruistic folks or
self-interested folks - that finite differencing error is probably the
limiting factor when we do p refinement on triangles or in 3D.
---
Roy
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