Convergence of a crystalline algorithmfor the heat equation in one dimensionand for the motion of a graphby weighted curvature

Pedro Martins Gir\~ao, Robert V. Kohn

Research output: Contribution to journalArticle

Abstract

Motion by (weighted) mean curvature is a geometric evolution law forsurfaces, representing steepest descent with respect to (an)isotropicsurface energy. It has been proposed that this motion couldbe computed by solving the analogous evolution law using a``crystalline'' approximation to the surface energy. We present thefirst convergence analysis for a numerical scheme of this type. Ourtreatment is restricted to one dimensional surfaces (curves in theplane) which are graphs. In this context, the scheme amounts to a newalgorithm for solving quasilinear parabolic equations in one spacedimension.

Original languageEnglish (US)
Pages (from-to)41-70
Number of pages30
JournalNumerische Mathematik
Volume67
Issue number1
DOIs
StatePublished - Feb 1994

Keywords

  • Mathematics Subject Classification (1991): 65M12, 73B30, 35K20

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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