TY - JOUR
T1 - A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization
AU - He , Yinnian
JO - Journal of Computational Mathematics
VL - 1
SP - 21
EP - 32
PY - 2004
DA - 2004/02
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8848.html
KW - Navier-Stokes equations, Mixed finite element, Error estimate, Finite element method.
AB - <p style="text-align: justify;">In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h &lt;&lt; H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy. &nbsp;</p>