Convergence of three iterative methods based on the finite element discretization for the stationary Navier–Stokes equations

This paper considers three iterative methods for solving the stationary Navier–Stokes equations. Iterative method I consists in solving the stationary Stokes equations, iterative method II consists in solving the stationary linearized Navier–Stokes equations and iterative method III consists in solving the stationary Oseen equations under the finite element discretization, respectively, at each iterative step. Also, we discuss the stability and convergence of three iterative methods. The iterative methods I and II are stability and convergence under the strong uniqueness conditions, where the iterative method II is the second order convergence. Furthermore, the iterative method III is uncondition stability and convergence under the uniqueness condition. Finally, some numerical tests show that the efficiency of the theoretical analysis.