Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements

Marie E. Rognes, Robert C. Kirby, Anders Logg
2010 SIAM Journal on Scientific Computing  
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
more » ... entation 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.
doi:10.1137/08073901x fatcat:u4rkyaimsngh7fd5jewc4g54fa