Novel $H^\mathrmdev(\mathrmCurl)$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model
<|reference_start|>Novel $H^\mathrmdev(\mathrmCurl)$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model: In this work we present a consistent reduction of the relaxed micromorphic model to its corresponding two-dimensional planar model, such that its capacity to capture discontinuous dilatation fields is preserved. As a direct consequence of our approach, new conforming finite elements for $H^\mathrm{dev}(\mathrm{Curl},A)$ become necessary. We present two novel $H^\mathrm{dev}(\mathrm{Curl},A)$-conforming finite element spaces, of which one is a macro element based on Clough--Tocher splits, as well as primal and mixed variational formulations of the planar relaxed micromorphic model. Finally, we demonstrate the effectiveness of our approach with two numerical examples.<|reference_end|>
@article{sky2024novel,
    title={Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming elements on regular
  triangulations and Clough--Tocher splits for the planar relaxed micromorphic
  model},
    author={Adam Sky, Michael Neunteufel, Peter Lewintan, Panos Gourgiotis,
  Andreas Zilian, Patrizio Neff},
    journal={arXiv preprint arXiv:2405.14849},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14849},
    primaryClass={math.NA cs.NA}
}