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

2016/12/02 by Klaus Deckelnick, Deckelnick, Klaus, Vanessa Styles +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1612.00789

openalex publication_date 2016/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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