Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913359921676288 |
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| author | Sky, Adam Neunteufel, Michael Lewintan, Peter Gourgiotis, Panos Zilian, Andreas Neff, Patrizio |
| author_facet | Sky, Adam Neunteufel, Michael Lewintan, Peter Gourgiotis, Panos Zilian, Andreas Neff, Patrizio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model Sky, Adam Neunteufel, Michael Lewintan, Peter Gourgiotis, Panos Zilian, Andreas Neff, Patrizio Numerical Analysis 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. |
| title | Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.14849 |