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

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 inter...

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Detalles Bibliográficos
Autores principales: Deckelnick, Klaus, Styles, Vanessa
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6004022/
https://www.ncbi.nlm.nih.gov/pubmed/29973742
http://dx.doi.org/10.1007/s00211-018-0946-6
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author Deckelnick, Klaus
Styles, Vanessa
author_facet Deckelnick, Klaus
Styles, Vanessa
author_sort Deckelnick, Klaus
collection PubMed
description 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.
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spelling pubmed-60040222018-07-02 Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface Deckelnick, Klaus Styles, Vanessa Numer Math (Heidelb) Article 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. Springer Berlin Heidelberg 2018-01-25 2018 /pmc/articles/PMC6004022/ /pubmed/29973742 http://dx.doi.org/10.1007/s00211-018-0946-6 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Deckelnick, Klaus
Styles, Vanessa
Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title_full Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title_fullStr Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title_full_unstemmed Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title_short Stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
title_sort stability and error analysis for a diffuse interface approach to an advection–diffusion equation on a moving surface
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6004022/
https://www.ncbi.nlm.nih.gov/pubmed/29973742
http://dx.doi.org/10.1007/s00211-018-0946-6
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AT stylesvanessa stabilityanderroranalysisforadiffuseinterfaceapproachtoanadvectiondiffusionequationonamovingsurface

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