In this paper, we present two-level defect-correction finite element method
for steady Navier-Stokes equations at high Reynolds number with the friction boundary
conditions, which results in a variational inequality problem of the second kind.
Based on Taylor-Hood element, we solve a variational inequality problem of NavierStokes
type on the coarse mesh and solve a variational inequality problem of NavierStokes
type corresponding to Newton linearization on the fine mesh. The error estimates
for the velocity in the H1 norm and the pressure in the L
2 norm are derived.
Finally, the numerical results are provided to confirm our theoretical analysis.