TY - JOUR T1 - Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem AU - An , Rong AU - Qiu , Hailong JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 36 EP - 54 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.11-m11188 UR - https://global-sci.org/intro/article_detail/aamm/56.html KW - Navier-Stokes equations, nonlinear slip boundary conditions, variational inequality problem, stabilized finite element, two-level methods. AB -

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 $h=\mathcal{O}(|\log h|^{1/2}H^3)$, 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.