Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems
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| Format: | Preprint |
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2025
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| _version_ | 1866909954075525120 |
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| author | Heimann, Fabian Lehrenfeld, Christoph Preuß, Janosch |
| author_facet | Heimann, Fabian Lehrenfeld, Christoph Preuß, Janosch |
| contents | We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry approximation of level set domains and has been presented and investigated computationally in [Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165]. Recently, in [Heimann, Lehrenfeld, IMA J. Numer. Anal., 2025] error bounds for the geometry approximation have been proven. In this paper we prove stability and accuracy including the influence of the geometry approximation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_08608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems Heimann, Fabian Lehrenfeld, Christoph Preuß, Janosch Numerical Analysis We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry approximation of level set domains and has been presented and investigated computationally in [Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165]. Recently, in [Heimann, Lehrenfeld, IMA J. Numer. Anal., 2025] error bounds for the geometry approximation have been proven. In this paper we prove stability and accuracy including the influence of the geometry approximation. |
| title | Discretization Error Analysis of a High Order Unfitted Space-Time Method for moving domain problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.08608 |