Two-level defect-correction locally stabilized finite element method for the steady Navier–Stokes equations

This paper proposes a two-level defect-correction stabilized finite element method for the steady Navier–Stokes equations based on local Gauss integration. The method combines the two-level strategy with the defect-correction method under the assumption of the uniqueness condition. Both the simplified and the Newton scheme are proposed and analyzed. Moreover, the numerical illustrations agree completely with the theoretical expectations.