Evolving finite elements for advection diffusion with an evolving interface
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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.04850
- arXiv:
- arXiv:2208.04850
- Bibcode:
- 2022arXiv220804850E
- Keywords:
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- Mathematics - Numerical Analysis
- E-Print:
- 32 pages, 5 figures, 1 table