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

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