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Efficient assembly of H(div) and H(curl) conforming finite elements

M.E. Rognes ; R.C. Kirby ; Anders Logg (Institutionen för matematiska vetenskaper, matematik)
SIAM Journal on Scientific Computing (1064-8275). Vol. 31 (2009), 6, p. 4130-4151.
[Artikel, refereegranskad vetenskaplig]

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. © 2009 Society for Industrial and Applied Mathematics.

Nyckelord: Mixed finite element , Piola , Variational form compiler

Denna post skapades 2014-01-05. Senast ändrad 2014-09-29.
CPL Pubid: 191169


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