Finite element error analysis for a system coupling surface evolution to diffusion on the surface

Deckelnick, Klaus and Styles, Vanessa (2022) Finite element error analysis for a system coupling surface evolution to diffusion on the surface. Interfaces and Free Boundaries. ISSN 1463-9963

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Abstract

We consider a numerical scheme for the approximation of a system that couples the evolution of a two-dimensional hypersurface to a reaction–diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to forced mean curvature flow. The method uses continuous, piecewise linear finite elements in space and a backward Euler scheme in time. Assuming the existence of a smooth solution, we prove optimal error bounds both in L∞(L2) and in L2(H1). We present several numerical experiments that confirm our theoretical findings and apply the method in order to simulate diffusion induced grain boundary motion.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 16 Jul 2021 07:05
Last Modified: 08 Feb 2022 12:15
URI: http://sro.sussex.ac.uk/id/eprint/100548

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