Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces

Abstract In this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the terms are only assumed to have locally Lipschitz derivatives. High-order surface finite elements used discretise weak system in space, and modified matrix–vector formulation for semi-discrete problem is derived. The anti-symmetric structure preserved by spatial discretisation. A new stability proof, based structure, combined consistency bounds proves optimal-order uniform-in-time error estimates. paper concluded variety numerical experiments.