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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2401.07807 |
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| _version_ | 1866916706720415744 |
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| author | Heimann, Fabian |
| author_facet | Heimann, Fabian |
| contents | We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preuß (SIAM J. Sci. Comput. 45(2), 2023, B139 - B165) for the bulk case with a method suggested by Sass, Reusken (Comput. Math. Appl. 146(15), 2023, 253-270) for the surface case. The geometry is allowed to change with time, and the higher order discrete approximation of this geometry is ensured by a time-dependent isoparametric mapping. The space-time discretisation approach allows for straightforward handling of arbitrary high orders. In that way, we also generalise results of Hansbo, Larson, Zahedi (Comput. Methods Appl. Mech. Engrg. 307, 2016, 96-116) to higher orders. The convergence of the proposed higher order discretisations is confirmed numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk problems Heimann, Fabian Numerical Analysis We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preuß (SIAM J. Sci. Comput. 45(2), 2023, B139 - B165) for the bulk case with a method suggested by Sass, Reusken (Comput. Math. Appl. 146(15), 2023, 253-270) for the surface case. The geometry is allowed to change with time, and the higher order discrete approximation of this geometry is ensured by a time-dependent isoparametric mapping. The space-time discretisation approach allows for straightforward handling of arbitrary high orders. In that way, we also generalise results of Hansbo, Larson, Zahedi (Comput. Methods Appl. Mech. Engrg. 307, 2016, 96-116) to higher orders. The convergence of the proposed higher order discretisations is confirmed numerically. |
| title | A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.07807 |