2000 character limit reached
Parametric finite element approximations of curvature driven interface evolutions (1903.09462v3)
Published 22 Mar 2019 in math.NA and cs.NA
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.