Some iterative finite element methods for steady Navier–Stokes equations with different viscosities

Two-level iterative finite element methods are designed to solve numerically the steady 2D/3D Navier–Stokes equations for a large viscosity ν such that a strong uniqueness condition holds. Moreover, the one-level Oseen iterative finite element method based on a fine mesh with small mesh size h is designed to solve numerically the steady 2D/3D Navier–Stokes equations for small viscosity ν such that a weak uniqueness condition holds. Meanwhile, the numerical investigations are provided to show that the proposed methods are efficient for solving the 2D/3D steady Navier–Stokes equations for different viscosities.