Two-level Methods Based on Three Corrections for the 2d/3d Steady Navier-stokes Equations

Two-level finite element methods are applied to solve numerically the 2D/3D steady Navier-Stokes equations if a strong uniqueness condition ( ‖f‖ −1 ‖f‖0 ) 1 2 ≤ δ = 1 − N‖f‖ −1 ν2 holds, where N is defined in (2.4)-(2.6). Moreover, one-level finite element method is applied to solve numerically the 2D/3D steady Navier-Stokes equations if a weak uniqueness condition 0 < δ < ( ‖f‖ −1 ‖f‖0 ) 1 2 holds. The two-level algorithms are motivated by solving a nonlinear problem on a coarse grid with mesh size H and computing the Stokes, Oseen and Newton correction on a fine grid with mesh size h << H. The uniform stability and convergence of these methods with respect to δ and grid sizes h and H are provided. Finally, some numerical tests are made to demonstrate the effectiveness of one-level method and the three two-level methods.