摘要
在求解鞍点问题的经典Uzawa算法收敛性的基础上,对预处理Uzawa算法收敛性做出进行进一步的研究,得到其收敛的充要条件及误差传播矩阵的谱半径;并将其应用到Mini元离散求解Stokes问题中,通过数值计算验证所得结论的正确性.
Based on the classical Uzawa algorithm for solving saddle point problems, the preconditioned Uzawa algorithm is studied. The necessary and sufficient conditions for convergence and the spectrum radius of the spread matrix of the preconditioned Uzawa algorithm are obtained. Applications to the Stokes equations by the Mini element, the theoretical results are verified by numerical calculations.
作者
孙国卿
朱晓云
郑权
SUN Guo-qing;ZHU Xiao-yun;ZHENG Quan(Mathematic Division, Tianjin University Ren Ai College, Tianjin 300072, China;Road and Bridge Engineering Department, Tianjin Transportation Vocational College, Tianjin 300110, China;College of Mathematics, North China University of Technology, Beijing 100144, China)
出处
《数学的实践与认识》
北大核心
2019年第10期268-272,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(11471019)
关键词
鞍点问题
预处理Uzawa算法
充要条件
STOKES问题
saddle point
preconditioned Uzawa algorithm
the necessary and sufficient condition
Stokes equations
