  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.
