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Finite element methods for fourth order axisymmetric geometric evolution equations

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Title: Finite element methods for fourth order axisymmetric geometric evolution equations
Authors: Barrett, JW
Garcke, H
Nürnberg, R
Item Type: Journal Article
Abstract: Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce and analyze several new finite element schemes for fourth order geometric evolution equations in an axisymmetric setting, and for selected schemes we will show existence, uniqueness and stability results. The presented schemes have very good mesh and stability properties, as will be demonstrated by several numerical examples.
Issue Date: 1-Jan-2019
Date of Acceptance: 1-Oct-2018
URI: http://hdl.handle.net/10044/1/65193
DOI: https://dx.doi.org/10.1016/j.jcp.2018.10.006
ISSN: 0021-9991
Publisher: Elsevier
Start Page: 733
End Page: 766
Journal / Book Title: Journal of Computational Physics
Volume: 376
Copyright Statement: © 2018 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Physics
Surface diffusion
Willmore flow
Helfrich flow
Finite elements
Axisymmetry
Tangential movement
SURFACE-DIFFUSION
SPONTANEOUS CURVATURE
NUMERICAL SCHEME
WILLMORE FLOW
APPROXIMATION
STABILITY
MOTION
DYNAMICS
ENERGY
math.NA
65M60, 65M12, 35K55, 53C44
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Notes: 45 pages, 26 figures. This article is closely related to arXiv:1805.04322
Publication Status: Published
Online Publication Date: 2018-10-09
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences