Coupled_MCF_graph - V Styles.pdf (829.3 kB)
Finite element error analysis for a system coupling surface evolution to diffusion on the surface
journal contribution
posted on 2023-06-10, 00:23 authored by Klaus Deckelnick, Vanessa StylesVanessa StylesWe 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.
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- Published
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- Accepted version
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Interfaces and Free BoundariesISSN
1463-9963Publisher
European Mathematical Society Publishing HouseExternal DOI
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- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2021-07-16First Open Access (FOA) Date
2022-02-08First Compliant Deposit (FCD) Date
2021-07-15Usage metrics
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