TY - JOUR
T1 - Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations
AU - Zhang , Tong
AU - Xu , Shunwei
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 19
EP - 35
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.11-m11178
UR - https://global-sci.org/intro/article_detail/aamm/55.html
KW - Stationary Navier-Stokes equations, finite volume method, two-level method, error
estimate.
AB - <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>