Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910711219748864 |
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| author | Reusken, Arnold Sass, Hauke |
| author_facet | Reusken, Arnold Sass, Hauke |
| contents | In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique of (iso)parametric mappings for which a level set representation of the evolving surface is essential. We derive basic results in which certain geometric characteristics of the exact space-time surface are related to corresponding ones of the numerical surface approximation. These results are used in an error analysis of a higher order space-time TraceFEM. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces Reusken, Arnold Sass, Hauke Numerical Analysis 65N12, 65N15, 65N30 In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique of (iso)parametric mappings for which a level set representation of the evolving surface is essential. We derive basic results in which certain geometric characteristics of the exact space-time surface are related to corresponding ones of the numerical surface approximation. These results are used in an error analysis of a higher order space-time TraceFEM. |
| title | Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces |
| topic | Numerical Analysis 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2401.01215 |