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

In this work we construct novel H(sym Curl)-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the div Div-sequence with respect to the H(sym Curl)-space. The elements respect H(Curl)-regularity and their lowest order versions converge optimally for [H(sym Curl) H(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.