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

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.