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arXiv · 2308.07750

Novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the relaxed micromorphic sequence

Adam Sky·Michael Neunteufel·Peter Lewintan·Andreas Zilian·Patrizio Neff
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Abstract

In this work we construct novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the $\mathrm{div} \mathrm{Div}$-sequence with respect to the $H(\mathrm{sym} \mathrm{Curl})$-space. The elements respect $H(\mathrm{Curl})$-regularity and their lowest order versions converge optimally for $[H(\mathrm{sym} \mathrm{Curl}) \setminus H(\mathrm{Curl})]$-fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model.

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Adam Sky, Michael Neunteufel, Peter Lewintan, Andreas Zilian, Patrizio Neff. 2023-08-15. Novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the relaxed micromorphic sequence. https://arxiv.org/abs/2308.07750

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