Conforming Finite Elements for $H(\text{sym}\,\text{Curl})$ and $H(\text{dev}\,\text{sym}\,\text{Curl})$

Abstract

We construct conforming finite elements for the spaces H(sym Curl) and H(dev sym Curl). Those are spaces of matrix-valued functions with symmetric or deviatoric-symmetric Curl in a Lebesgue space, and they appear in various models of nonstandard solid mechanics. The finite elements are not H(Curl)-conforming. We show the construction, prove conformity and unisolvence, and point out optimal approximation error bounds.

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BGG sequences with weak regularity and applications

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