A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves

A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can preserve two geometric structures simultaneously in the discrete...

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Bibliographic Details
Published inJournal of computational physics Vol. 443; p. 110531
Main Authors Jiang, Wei, Li, Buyang
Format Journal Article
LanguageEnglish
Published Cambridge Elsevier Inc 15.10.2021
Elsevier Science Ltd
Subjects
Algorithms
Area conservation
Computational physics
Finite element method
Parametric
Perimeter decrease
Surface diffusion
Surface diffusion flow
Time stepping
Area conservation
Finite element method
Parametric
Surface diffusion flow
Perimeter decrease
Time stepping
Online AccessGet full text
ISSN0021-9991
1090-2716
1090-2716
DOI10.1016/j.jcp.2021.110531

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Summary:A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can preserve two geometric structures simultaneously in the discrete level, i.e., the perimeter of the curve decreases in time while the area enclosed by the curve is conserved. Numerical examples are provided to demonstrate the convergence of the proposed method and the effectiveness of the method in preserving the two geometric structures.
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ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2021.110531