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 hh, even for regular triangulations. A series of numerical examples are provided to illustrate the computational performance of the method.