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