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arXiv · 2405.11984

A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential

Charles M. Elliott·Thomas Sales
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Abstract

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.

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Charles M. Elliott, Thomas Sales. 2025-02-11. A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential. https://doi.org/10.1007/s00211-025-01457-8

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