Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface

Deckelnick, Klaus and Styles, Vanessa (2018) Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface. Numerische Mathematik. ISSN 0029-599X

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Abstract

In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Vanessa Styles
Date Deposited: 16 Jan 2018 08:11
Last Modified: 29 Jan 2018 14:13
URI: http://sro.sussex.ac.uk/id/eprint/72881

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