Novel H(symCurl)-conforming finite elements for the relaxed micromorphic sequence

Sky, Neunteufel, Lewintan, Zilian, Neff Computer Methods in Applied Mechanics and Engineering, 2024, (preprint)

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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