%0 Journal Article
%T Efficient Assembly of H(div) and H(curl) Conforming Finite Elements
%A Marie Rognes
%A Robert C. Kirby
%A Anders Logg
%J Mathematics
%D 2012
%I arXiv
%R 10.1137/08073901X
%X In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor and a mesh-dependent geometry tensor. Two key points must then be considered: the appropriate mapping of basis functions from a reference element, and the orientation of geometrical entities. To address these issues, we extend here a previously presented representation theorem for affinely mapped elements to Piola-mapped elements. We also discuss a simple numbering strategy that removes the need to contend with directions of facet normals and tangents. The result is an automated, efficient, and easy-to-use implementation that allows a user to specify finite element variational forms on H(div) and H(curl) in close to mathematical notation.
%U http://arxiv.org/abs/1205.3085v1