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arXiv · 2411.05650

An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential

Charles M. Elliott·Thomas Sales
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Abstract

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.

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Charles M. Elliott, Thomas Sales. 2024-11-08. An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential. https://arxiv.org/abs/2411.05650

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