Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem
Year: 2000
Author: Qing-Ping Deng, Xue-Jun Xu, Shu-Min Shen
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 2 : pp. 141–156
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2000-JCM-9030
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 2 : pp. 141–156
Published online: 2000-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Navier-Stokes problem P1 nonconforming element Maximum Norm.