Geodesic
Finite element error analysis for a system coupling surface evolution to diffusion on the surface
Klaus Deckelnick1 ; Vanessa Styles2
1Otto-von-Guericke-Universität Magdeburg, Germany
2University of Sussex, Brighton, UK
Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 63-93

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DOI

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.
DOI : 10.4171/ifb/467
Classification : 65-XX, 35-XX
Mots-clés : Surface PDE, forced mean curvature flow, diffusion induced grain boundary motion, finite elements, error analysis

Klaus Deckelnick  1   ; Vanessa Styles  2

1 Otto-von-Guericke-Universität Magdeburg, Germany
2 University of Sussex, Brighton, UK 
Klaus Deckelnick; Vanessa Styles. Finite element error analysis for a system coupling surface evolution to diffusion on the surface. Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 63-93. doi: 10.4171/ifb/467
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