Elliott, CM, Ranner, T orcid.org/0000-0001-7682-3175 and Stepanov, P (2022) Evolving finite elements for advection diffusion with an evolving interface. [Preprint - arXiv]
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:https://doi.org/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.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jun 2024 09:42 |
Last Modified: | 03 Jun 2024 09:42 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:190050 |