Volume 18, Issue 2
Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem

Qing Ping Deng, Xue Jun Xu & Shu Min Shen

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J. Comp. Math., 18 (2000), pp. 141-156

Published online: 2000-04

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  • 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.

  • Keywords

Navier-Stokes problem P1 nonconforming element Maximum Norm

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@Article{JCM-18-141, author = {}, title = {Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {2}, pages = {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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9030.html} }
TY - JOUR T1 - Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem JO - Journal of Computational Mathematics VL - 2 SP - 141 EP - 156 PY - 2000 DA - 2000/04 SN - 18 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/9030.html KW - Navier-Stokes problem KW - P1 nonconforming element KW - Maximum Norm AB - 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.
Qing Ping Deng, Xue Jun Xu & Shu Min Shen. (1970). Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem. Journal of Computational Mathematics. 18 (2). 141-156. doi:
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