Robust Finite Elements for linearized Magnetohydrodynamics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916079131951104 |
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| author | da Veiga, L. Beirão Dassi, F. Vacca, G. |
| author_facet | da Veiga, L. Beirão Dassi, F. Vacca, G. |
| contents | We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a non-conforming BDM approach with suitable DG terms for the fluid part, combined with an $H^1$-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15478 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust Finite Elements for linearized Magnetohydrodynamics da Veiga, L. Beirão Dassi, F. Vacca, G. Numerical Analysis We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a non-conforming BDM approach with suitable DG terms for the fluid part, combined with an $H^1$-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments. |
| title | Robust Finite Elements for linearized Magnetohydrodynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2306.15478 |