TY - JOUR T1 - Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions AU - Liu , An AU - Li , Yuan AU - An , Rong JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 932 EP - 952 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m595 UR - https://global-sci.org/intro/article_detail/aamm/12124.html KW - Navier-Stokes equations, friction boundary conditions, variational inequality problems, defect-correction method, two-level mesh method. AB -

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.