Evolving finite elements for advection diffusion with an evolving interface
Provides a rigorous numerical framework for solving advection-diffusion problems with moving interfaces, benefiting computational scientists working on interface evolution.
The paper develops a numerical scheme for parabolic evolving interface problems using evolving finite elements, proving optimal order error bounds and verifying convergence with numerical experiments.
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 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.