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.
This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing some open ball BR, and the nonlinear problem in the bounded domain and the linearized problem in the new exterior domain are considered and the approximation coupled problem is obtained. We show that the error between the solution u of Navier-Stokes equations around a rotating obstacle and the solution ue of the approximation coupled problem is O（R-1/4） in the Hl-seminorm when Iwl does not exceed some constant.
