English

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.

Keywords

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)

R2 v1 2026-06-28T16:33:01.903Z