Evolving finite elements for advection diffusion with an evolving interface
Numerical Analysis
2026-05-15 v3 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2208.04850,
title = {Evolving finite elements for advection diffusion with an evolving interface},
author = {C. M. Elliott and T. Ranner and P. Stepanov},
journal= {arXiv preprint arXiv:2208.04850},
year = {2026}
}