@Article{AAMM-5-1,
author = {Rong, An and Qiu, Hailong},
title = {Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2013},
volume = {5},
number = {1},
pages = {36--54},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.11-m11188},
url = {https://global-sci.com/article/73478/two-level-newton-iteration-methods-for-navier-stokes-type-variational-inequality-problem}
}