On two-level Oseen iterative methods for the 2D/3D steady Navier-Stokes equations

Oseen iterative method is applied for solving numerically steady 2D/3D Navier-Stokes equations with respect to small viscosity ν. Several combination strategies of Oseen iterative method and two-level finite element algorithms are applied to solve numerically the steady 2D/3D Navier-Stokes equations in terms of different viscosity ν or viscosity-dependent equivalent conditions. These combination strategies are motivated by applying Oseen iterations of m times for a nonlinear problem on a coarse grid with mesh size H and computing some linearised problems on a fine grid with mesh size h. The corresponding error analyses are performed and the error estimate results are shown. Finally, numerical tests and comparisons are made to demonstrate the effectiveness of the Oseen iterative method and the two-level Oseen iterative methods. Moreover, the comprehensive assessments about the proposed strategies are made.