Two-level defect-correction stabilized finite element method for Navier–Stokes equations with friction boundary conditions

In this paper, we consider a two-level defect-correction stabilized finite element method (DCSFEM) for the incompressible Navier–Stokes equation with friction boundary conditions based on local Gauss integration. The main idea is to combine the two-level strategy with the defect-correction method. Using this technique, the simplified two-level DCSFEM and the Newton two-level DCSFEM are proposed and some error estimates are derived. Finally, the numerical results are displayed to confirm our theoretical findings.