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.

翻译：我们研究了在演化曲面上求解具有多项式增长光滑势的Cahn-Hilliard方程的两种完全离散演化曲面有限元格式。特别地，我们针对（完全隐式）后向欧拉时间离散化以及隐式-显式时间离散化，结合等参曲面有限元空间离散化，建立了最优阶误差估计。