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

Pedro Martins Gir\~ao, Robert 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 - 1994

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Interfacial energy
Heat Equation
Curvature
Crystalline materials
Weighted Mean
Quasilinear Parabolic Equations
Steepest Descent
Motion
Surface Energy
Mean Curvature
Convergence Analysis
Numerical Scheme
Curve
Approximation
Graph in graph theory
Energy
Hot Temperature
Context

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Convergence of a crystalline algorithmfor the heat equation in one dimensionand for the motion of a graphby weighted curvature. / Gir\~ao, Pedro Martins; Kohn, Robert.

In: Numerische Mathematik, Vol. 67, No. 1, 1994, p. 41-70.

Research output: Contribution to journalArticle

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