Uzawa iteration method for stokes type variational inequality of the second kind

作者：Li, Yuan^*; Li, Kai-tai

来源：Acta Mathematicae Applicatae Sinica-English Series, 2011, 27(2): 303-316.

DOI：10.1007/s10255-011-0063-0

• Stokes problem
• nonlinear slip boundary
• variational inequality
• Uzawa iteration 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 L. 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.

• 单位
  温州大学; 西安交通大学