Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we present two-level defect-correction finite element methodfor steady Navier-Stokes equations at high Reynolds number with the friction boundaryconditions, which results in a variational inequality problem of the second kind.Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokestype on the coarse mesh and solve a variational inequality problem of Navier-Stokestype corresponding to Newton linearization on the fine mesh. The error estimatesfor 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.