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

Wei Jiang, Buyang Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 languageEnglish
Article number110531
Pages (from-to)1-11
Number of pages11
JournalJournal of Computational Physics
Volume443
DOIs
Publication statusPublished - 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)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this