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：我们研究了两种用于演化曲面上Cahn-Hilliard方程的全离散演化曲面有限元格式，其中光滑势具有多项式增长特性。特别地，我们针对采用等参曲面有限元离散空间的全隐式向后欧拉时间离散格式和隐式-显式时间离散格式，建立了最优阶误差界。