The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1093/imanum/draa062). An appropriate weak formulation of the problem is derived for the use of evolving finite elements designed to accommodate for a moving interface. Optimal order error bounds are proved for arbitrary order evolving isoparametric finite elements. The paper concludes with numerical results for a model problem verifying orders of convergence.

翻译：本文旨在基于（C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1093/imanum/draa062）提出的抽象演化有限元框架，开发一种近似求解抛物型方程演化界面问题的数值方案。针对移动界面，推导了适用于演化有限元的适当弱形式。对于任意阶的演化等参有限元，证明了最优阶误差界。最后通过模型问题的数值结果验证了收敛阶。