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math.NA2021
Finite element error analysis for a system coupling surface evolution to diffusion on the surface
Klaus Deckelnick, Vanessa 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…
math.NA2020
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces
Klaus Deckelnick, Robert Nürnberg
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the…
math.NA2020
A Practical Phase Field Method for an Elliptic Surface PDE
John W. Barrett, Klaus Deckelnick, Vanessa Styles
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadr…