@Article{AAMM-5-19,
author = {Zhang , Tong and Xu , Shunwei},
title = {Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2013},
volume = {5},
number = {1},
pages = {19--35},
abstract = {<p style="text-align: justify;">In this work, two-level stabilized finite volume formulations for the
2D steady Navier-Stokes equations are considered.
These methods are based
on the local Gauss integration technique and the lowest equal-order
finite element pair. Moreover, the two-level
stabilized finite volume methods involve solving one small Navier-Stokes
problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and
Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite
volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.
These methods we studied provide an
approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order
as the standard stabilized finite volume method, which involve solving one large
nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods
can save a large amount of computational time.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.11-m11178},
url = {http://global-sci.org/intro/article_detail/aamm/55.html}
}