Parametric finite element approximations of curvature driven interface evolutions
File(s)
Working paper
Author(s)
Barrett, John W
Garcke, Harald
Nürnberg, Robert
Type
Working Paper
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.
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.
Date Issued
2019-03-22
Citation
2019
Publisher
arXiv
Copyright Statement
© 2019 The Author(s).
Identifier
http://arxiv.org/abs/1903.09462v1
Subjects
math.NA
math.NA
65M60, 53C44, 35K55, 65M12, 74E10, 74N05, 76D05, 92C05
Notes
139 pages, 7 figures
Publication Status
Published