Two algorithms for two-phase Stefan type problems  

作　　者：LIAN Xiao-peng CHENG Xiao-liang HAN Wei-min 

机构地区：[1]Dept. of Math., Zhejiang Univ., Hangzhou 310027, China [2]Dept. of Math., University of Iowa, Iowa City, IA 52242, USA

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2009年第3期298-308,共11页高校应用数学学报（英文版）（B辑）

基　　金：supported by the National Natural Science Foundation (10871179) of China

摘　　要：In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.

关 键 词：relaxation method Uzawa algorithm variational inequality two-phase Stefan type problem 

分 类 号：O153.3[理学—数学] TP18[理学—基础数学]