A two-level subgrid stabilized Oseen iterative method for the steady Navier–Stokes equations

Based on two-grid finite element discretization and a recent subgrid-scale model, a two-level subgrid stabilized Oseen iterative method for the convection dominated Navier–Stokes equations is proposed and analyzed. This method combines the best algorithmic features of the two-grid discretization and subgrid stabilization methods. It first solves a subgrid stabilized nonlinear Navier–Stokes problem by applying m Oseen iterations on a coarse grid, and then solves a linear problem on a finer grid where the nonlinear convection term is fixed by the coarse grid solution. Stability of the method and error estimates of the discrete solution are analyzed. The algorithmic parameter scalings are also derived. Numerical results on an example with known analytical solution, the lid-driven cavity flow and the backward-facing step flow are given to verify the theoretical predictions and demonstrate the method’s promise.