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
收藏
页码：1103 / 1125
页数：23
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