Optimal Rate of Convergence of the Bence-Merriman-Osher Algorithm for Motion by Mean Curvature

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説明

Bence, Merriman, and Osher proposed an algorithm for computing the motion a hypersurface by mean curvature in terms of solutions of the usual heat equation, continually reinitialized after short time steps. In this paper, applying some techniques of asymptotic analysis for the Allen--Cahn equation, we give a rate of convergence of their algorithm for the motion of a smooth and compact hypersurface by mean curvature. We also consider the special case of a circle evolving by curvature and show that our rate is optimal.

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詳細情報 詳細情報について

  • CRID
    1050856995325515904
  • NII論文ID
    120000949789
  • DOI
    10.1137/04061862x
  • ISSN
    10957154
    00361410
  • HANDLE
    20.500.14094/90000302
  • 本文言語コード
    en
  • 資料種別
    journal article
  • データソース種別
    • IRDB
    • CiNii Articles
    • OpenAIRE

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