Uzawa Iteration Method for Stokes Type Variational Inequality of the Second Kind  

作　　者：Yuan Li Kai-tai Li 

机构地区：[1]College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China [2]College of Science, Xi'an Jiaotong University, Xi'an 710049, China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第2期303-316,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10571142,No.10701061,No.10901122, No.10971165 and No.11001205)

摘　　要：In this paper, the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind. Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity. Moreover, the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional ζ. Subsequently, the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate. Finally, we give the numerical results to verify the feasibility of the Uzawa algorithm.In this paper, the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind. Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity. Moreover, the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional ζ. Subsequently, the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate. Finally, we give the numerical results to verify the feasibility of the Uzawa algorithm.

关 键 词：Stokes problem nonlinear slip boundary variational inequality Uzawa iteration algorithm 

分 类 号：O176[理学—数学] O241.82[理学—基础数学]