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 h, even for regular triangulations. A series of numerical experiments are reported to show the computational performance and accuracy of our methods proposed. (C) 2014 Elsevier B.V. All rights reserved.