(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
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 Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the H^1 norm and the pressure in the L^2 norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.