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

by Deckelnick, K.; Styles, V..

Series: 2016-10, Preprints

65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
35R05 Partial differential equations with discontinuous coefficients or data

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.

finite elements; PDEs on surfaces; phase field approximation; error bounds