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

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posted on 2023-06-21, 06:02 authored by Klaus Deckelnick, Vanessa StylesVanessa Styles
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Numerische Mathematik

ISSN

0029-599X

Publisher

Springer Verlag

Issue

3

Volume

139

Page range

709-741

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-01-16

First Open Access (FOA) Date

2018-01-29

First Compliant Deposit (FCD) Date

2018-01-15

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