Novel $H(\mathrm{s}\mathrm{y}\mathrm{m}\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})$-conforming finite elements for the relaxed micromorphic sequence

In this work we construct novel $H(\mathrm{s}\mathrm{y}\mathrm{m}\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})$-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the $\mathrm{d}\mathrm{i}\mathrm{v}\mathrm{D}\mathrm{i}\mathrm{v}$-sequence with respect to the $H(\mathrm{s}\mathrm{y}\mathrm{m}\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})$-space. The elements respect $H(\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})$-regularity and their lowest order versions converge optimally for $[H(\mathrm{s}\mathrm{y}\mathrm{m}\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})\setminus H(\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l})]$-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.