A simplified two-level method for the steady Navier–Stokes equations Original Research Article

A simplified two-level method for solving the steady two-dimensional incompressible Navier–Stokes equations is investigated in this article. The simplified two-level method involves solving one small nonlinear Navier–Stokes problem on the coarse mesh and one linear Stokes problem (hence, linear with positive definite symmetric part) on the fine mesh. The uniform optimal error estimates with respect to large image for the standard Galerkin method and the two-level method are proven. Finally, some numerically tests to confirm the theoretical results of the simplified two-level method and the standard Galerkin method are provided.