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