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

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posted on 2023-06-10, 00:23 authored by Klaus Deckelnick, Vanessa StylesVanessa Styles
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 L8(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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Interfaces and Free Boundaries

ISSN

1463-9963

Publisher

European Mathematical Society Publishing House

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-07-16

First Open Access (FOA) Date

2022-02-08

First Compliant Deposit (FCD) Date

2021-07-15

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