A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential
Numerical Analysis
2025-03-14 v2 Numerical Analysis
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.
Cite
@article{arxiv.2405.11984,
title = {A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential},
author = {Charles M. Elliott and Thomas Sales},
journal= {arXiv preprint arXiv:2405.11984},
year = {2025}
}
Comments
42 pages, 5 figures (added new section on sharp interface numerics)