Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem (Advances in Applied Mathematics and Mechanics, 2018)
This paper deals with thetwo-level Newton iteration method based on the pressure projectionstabilized finite element approximation to solve the numerical solution ofthe Navier-Stokes type variational inequality problem. We solve a smallNavier-Stokes problem on the coarse mesh with mesh size $H$ and solve a large linearized Navier-Stokes problem on thefine mesh with mesh size $h$. The error estimates derived show thatif we choose $h=\mathcal{O}(|\log h|^{1/2}H^3)$, then the two-level method weprovide 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.