Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model
Numerical Analysis
2024-05-24 v1 Numerical Analysis
Abstract
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 become necessary. We present two novel -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.
Cite
@article{arxiv.2405.14849,
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 and Michael Neunteufel and Peter Lewintan and Panos Gourgiotis and Andreas Zilian and Patrizio Neff},
journal= {arXiv preprint arXiv:2405.14849},
year = {2024}
}