TY - JOUR
T1 - Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem
AU - Deng , Qing-Ping
AU - Xu , Xue-Jun
AU - Shen , Shu-Min
JO - Journal of Computational Mathematics
VL - 2
SP - 141
EP - 156
PY - 2000
DA - 2000/04
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9030.html
KW - Navier-Stokes problem, P1 nonconforming element, Maximum Norm.
AB - <p style="text-align: justify;">This paper deals with Crouzeix-Raviart nonconforming finite element approximation of Navier-Stokes equation in a plane bounded domain, by using the so-called velocity-pressure mixed formulation. The quasi-optimal maximum norm error estimates of the velocity and its first derivatives and of the pressure are derived for nonconforming C-R scheme of stationary Navier-Stokes problem. The analysis is based on the weighted inf-sup condition and the technique of weighted Sobolev norm. By the way, the optimal $L^2$-error estimate for nonconforming finite element approximation is obtained.</p>