Some Uzawa methods for steady incompressible Navier-Stokes equations discretized by mixed element methods

Numerical solutions of Navier-Stokes equations play fundamental roles in scientific computing and fluid mechanics. In this talk, I am going to present some Uzawa-type iterative methods for solving the steady incompressible Navier-Stokes equations discretized by mixed element methods. Compared with most existing iterative methods, these methods require no numerical solution of any saddle-point system at each iterative step. After some novel and technical derivation, it is proved that the methods converge geometrically with a contraction number independent of the finite element mesh size $h$, even for regular triangulations. A series of numerical experiments are reported to show the computational performance and accuracy of our methods proposed. This is a joint work with Puyin Chen and Huashan Sheng.