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

Some Uzawa-type iterative methods are devised to solve steady incompressible Navier–Stokes equations discretized by mixed element methods. Compared with the most existing iterative methods, these methods require no numerical solution of any saddle-point system at each iteration 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 hh, even for regular triangulations. A series of numerical experiments are reported to show the computational performance and accuracy of our methods proposed.