A Perimeter-decreasing and Area-conserving Algorithm for Surface Diffusion Flow of Curves

Wei Jiang; Buyang Li

doi:10.1016/j.jcp.2021.110531

A Perimeter-decreasing and Area-conserving Algorithm for Surface Diffusion Flow of Curves

Wei Jiang, Buyang Li

Research output: Journal article publication › Journal article › Academic research › peer-review

20 Citations (Scopus)

Abstract

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.

Original language	English
Article number	110531
Pages (from-to)	1-11
Number of pages	11
Journal	Journal of Computational Physics
Volume	443
DOIs	https://doi.org/10.1016/j.jcp.2021.110531
Publication status	Published - 15 Oct 2021

Keywords

Area conservation
Finite element method
Parametric
Perimeter decrease
Surface diffusion flow
Time stepping

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

More information

10.1016/j.jcp.2021.110531

http://hdl.handle.net/10397/93846

Cite this

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abstract = "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.",

keywords = "Area conservation, Finite element method, Parametric, Perimeter decrease, Surface diffusion flow, Time stepping",

author = "Wei Jiang and Buyang Li",

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N2 - 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.

AB - 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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KW - Parametric

KW - Perimeter decrease

KW - Surface diffusion flow

KW - Time stepping

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JO - Journal of Computational Physics

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A Perimeter-decreasing and Area-conserving Algorithm for Surface Diffusion Flow of Curves

Abstract

Keywords

ASJC Scopus subject areas

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