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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月12日

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  • Charles M. Elliott,
  • Thomas Sales

摘要

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.