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.

翻译：本文针对近期提出的松弛微形态序列构造了新的$H(\mathrm{sym} \mathrm{Curl})$协调有限元。该序列可视为$\mathrm{div} \mathrm{Div}$序列关于$H(\mathrm{sym} \mathrm{Curl})$空间的完备化。所构造单元满足$H(\mathrm{Curl})$正则性，且其最低阶版本对$[H(\mathrm{sym} \mathrm{Curl}) \setminus H(\mathrm{Curl})]$场具有最优收敛性。本文详细介绍了构造过程、基函数的线性无关性证明与协调性分析，并给出了数值算例。此外，我们展示了该单元在松弛微形态模型超材料计算中的应用。