TY - JOUR
T1 - A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization
AU - He , Yinnian
AU - Miao , Huanling
AU - Ren , Chunfeng
JO - Journal of Computational Mathematics
VL - 1
SP - 33
EP - 54
PY - 2004
DA - 2004/02
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8849.html
KW - Navier-Stokes equations, Galerkin method, Finite element.
AB - <p style="text-align: justify;">&nbsp;In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h &lt;&lt; H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method. &nbsp;</p>