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 - <p style="text-align: justify;">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.</p>