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arXiv · 1205.3085

Efficient Assembly of H(div) and H(curl) Conforming Finite Elements

Marie Rognes·Robert C. Kirby·Anders Logg
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Abstract

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.

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Marie Rognes, Robert C. Kirby, Anders Logg. 2012-05-14. Efficient Assembly of H(div) and H(curl) Conforming Finite Elements. https://doi.org/10.1137/08073901x

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