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

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 = {Qing-Ping Deng , and Xue-Jun Xu , and Shu-Min Shen , }, 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 AU - Qing-Ping Deng , AU - Xue-Jun Xu , AU - Shu-Min Shen , 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 -

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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