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Parametric finite element approximations of curvature driven interface evolutions

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1903.09462v1.pdfWorking paper2.92 MBAdobe PDFView/Open
Title: Parametric finite element approximations of curvature driven interface evolutions
Authors: Barrett, JW
Garcke, H
Nürnberg, R
Item 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.
Issue Date: 22-Mar-2019
URI: http://hdl.handle.net/10044/1/73024
Publisher: arXiv
Copyright Statement: © 2019 The Author(s).
Keywords: math.NA
math.NA
65M60, 53C44, 35K55, 65M12, 74E10, 74N05, 76D05, 92C05
math.NA
math.NA
65M60, 53C44, 35K55, 65M12, 74E10, 74N05, 76D05, 92C05
Notes: 139 pages, 7 figures
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics