Two-Grid Arrow-Hurwicz Methods for the Steady Incompressible Navier-Stokes Equations

In this paper, three kinds of two-grid Arrow-Hurwicz (A-H) methods are proposed and analyzed for the steady incompressible Navier-Stokes equations, which adopt the existing A-H method to obtain the coarse mesh solution, and further enhance the efficiency by three different one-step schemes (Oseen type, Simple type and Newton type) on the fine mesh. These methods combine the A-H method and the two-grid strategy, retaining the best features of two techniques and overcoming some of their limitations. Furthermore, the error analyses of the three methods are carefully studied and the numerical tests are reported to demonstrate the theoretical results and show the efficiency of the methods.