A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917954243788800 |
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| author | Elliott, Charles M. Sales, Thomas |
| author_facet | Elliott, Charles M. Sales, Thomas |
| contents | We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully implicit) backward Euler time-discretisation, and an implicit-explicit time-discretisation, with isoparametric surface finite elements discretising space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential Elliott, Charles M. Sales, Thomas Numerical Analysis 65M60 (Primary), 65M15, 35K58 (Secondary) We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully implicit) backward Euler time-discretisation, and an implicit-explicit time-discretisation, with isoparametric surface finite elements discretising space. |
| title | A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential |
| topic | Numerical Analysis 65M60 (Primary), 65M15, 35K58 (Secondary) |
| url | https://arxiv.org/abs/2405.11984 |