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Remarks on the convergence of an algorithm for curvature-dependent motions of hypersurfaces

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    *Corresponding author 
The first author is supported by JSPS KAKENHI Grant Numbers JP17K05364 and JP252470080.
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  • We consider a threshold-type algorithm for curvature-dependent motions (CDM for short) of hypersurfaces. This algorithm was numerically studied by Kimura - Notsu [13], Esedoḡlu - Ruuth - Tsai [7] and Mohammad - Švadlenka [16], where they used the signed distance function as the level set function for CDM. The convergence of this algorithm and its optimal rate have been considered in Ishii - Kimura [12]. In this paper we give different approaches to the optimal rate of convergence to the smooth and compact CDM from [12]. As for the optimality, we give a more precise estimate than that in [12].

    Mathematics Subject Classification: Primary: 35K15, 35K55; Secondary: 65M12.


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  • Figure 1.  Graphs of $ w_k $, $ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{w}_k $ and $ \bar{w}_k $ (thick curves)

    Figure 2.  Graphs of of $ w^k $, $ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{w}^k $ and $ \bar{w}^k $ (thick curves)

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