(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem. We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h. The error estimates derived show that if we choose h=O(|h|^1/2H^3), then the two-level method we provide has the same H^1 and L^2 convergence orders of the velocity and the pressure as the one-level stabilized method. However, the L^2 convergence order of the velocity is not consistent with that of one-level stabilized method. Finally, we give the numerical results to support the theoretical analysis.