Solving steady incompressible Navier-Stokes equations by the Arrow-Hurwicz method

This article is devoted to analyzing an Arrow-Hurwicz type method for solving incompressible Navier-Stokes equations discretized by mixed element methods. Under several reasonable conditions, it is proved by a subtle argument that the method converges geometrically with a contraction number independent of the finite element mesh size h, even for regular triangulations. A series of numerical examples are provided to illustrate the computational performance of the method. (C) 2016 Elsevier B.V. All rights reserved.