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Optimal Rate of Convergence of the Bence-Merriman-Osher Algorithm for Motion by Mean Curvature
Description
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.
Journal
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- SIAM Journal on Mathematical Analysis
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SIAM Journal on Mathematical Analysis 37 (3), 841-866, 2006
Society for Industrial and Applied Mathematics (SIAM)
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Details 詳細情報について
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- CRID
- 1050856995325515904
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- NII Article ID
- 120000949789
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- ISSN
- 10957154
- 00361410
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- HANDLE
- 20.500.14094/90000302
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- CiNii Articles
- OpenAIRE
