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

In this paper, we consider a defect-correction stabilized finite element method for incompressible Navier–Stokes equations with friction boundary conditions whose variational formulation is the variational inequality problem of the second kind with Navier–Stokes operator. In the defect step, an artificial viscosity parameter σ   is added to the Reynolds number as a stability factor, and the Oseen iterative scheme is applied in the correction step. H1×L2H1×L2 error estimations are derived for the one-step defect-correction stabilized finite element method. In the end, some numerical results are presented to verify the theoretical analysis.