From: Roy Stogner <roystgnr@ic...>  20110124 22:38:16

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 1e5 to 1e11 at several > quadrature points which is though small but nonzero. 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 selfinterested folks  that finite differencing error is probably the limiting factor when we do p refinement on triangles or in 3D.  Roy 