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arXiv · 1903.09462

Parametric finite element approximations of curvature driven interface evolutions

John W. Barrett·Harald Garcke·Robert Nürnberg
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Abstract

Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature. The approaches discussed, in contrast to many other methods, have good mesh properties that avoid mesh coalescence and very non-uniform meshes. Mean curvature flow, surface diffusion, anisotropic geometric flows, solidification, two-phase flow, Willmore and Helfrich flow as well as biomembranes are treated. We show stability results as well as results explaining the good mesh properties.

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John W. Barrett, Harald Garcke, Robert Nürnberg. 2019-03-22. Parametric finite element approximations of curvature driven interface evolutions. https://doi.org/10.1016/bs.hna.2019.05.002

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