REMARKS ON THE CONVERGENCE OF AN ALGORITHM FOR CURVATURE-DEPENDENT MOTIONS OF HYPERSURFACES

被引：0

作者：

Ishii, Katsuyuki ^{[1
]}

Izumi, Takahiro ^{[2
]}

机构：

[1] Kobe Univ, Grad Sch Maritime Sci, Higashinada Ku, Kobe, Hyogo 6580022, Japan

[2] Yasuna Machine Designing, Himeji, Hyogo 6700945, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 03期

关键词：

Threshold-type algorithm; curvature-dependent motion; rate of convergence; SIGNED DISTANCE FUNCTION; MEAN-CURVATURE; APPROXIMATION SCHEME; FLOW; SETS;

D O I：

10.3934/dcds.2018046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a threshold-type algorithm for curvature-dependent motions (CDM for short) of hypersurfaces. This algorithm was numerically studied by Kimura - Notsu [13], Esedoglu - Ruuth - Tsai H and Mohammad - Svadlenka [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].

引用

页码：1103 / 1125

页数：23

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