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.

本文针对稳态不可压缩Navier-Stokes方程，提出并分析了三种二网格Arrow-Hurwicz(AH)方法，它们采用现有的AH方法获得粗网格解，并进一步提高了三个效率。细网格上的不同一步方案（Oseen 型、简单型和牛顿型）。这些方法结合了AH方法和双网格策略，保留了两种技术的最佳特性并克服了它们的一些局限性。此外，仔细研究了三种方法的误差分析，并报告了数值试验，以证明理论结果并显示方法的有效性。