An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915487850430464 |
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| author | Elliott, Charles M. Sales, Thomas |
| author_facet | Elliott, Charles M. Sales, Thomas |
| contents | In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time discretisation. Our analysis relies on a specific geometric assumption on the evolution of the surface. Our main results are $L^2_{H^1}$ error bounds for both the semi-discrete and fully discrete schemes, and we provide some numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential Elliott, Charles M. Sales, Thomas Numerical Analysis 65M60 (Primary) 65M16, 35K67 (Secondary) In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time discretisation. Our analysis relies on a specific geometric assumption on the evolution of the surface. Our main results are $L^2_{H^1}$ error bounds for both the semi-discrete and fully discrete schemes, and we provide some numerical results. |
| title | An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential |
| topic | Numerical Analysis 65M60 (Primary) 65M16, 35K67 (Secondary) |
| url | https://arxiv.org/abs/2411.05650 |