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An error estimate for two-dimensional Stokes driven cavity flow


Authors: Zhiqiang Cai and Yanqiu Wang
Journal: Math. Comp. 78 (2009), 771-787
MSC (2000): Primary 65N15, 65N30, 76D07
DOI: https://doi.org/10.1090/S0025-5718-08-02177-7
Published electronically: October 1, 2008
MathSciNet review: 2476559
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Abstract: Discontinuous velocity boundary data for the lid driven cavity flow has long been causing difficulties in both theoretical analysis and numerical simulations. In finite element methods, the variational form for the driven cavity flow is not valid since the velocity is not in $ \boldsymbol{H}^1$. Hence standard error estimates do not work. By using only $ \mathbf{W}^{1,r}$ $ (1<r< 2)$ regularity and constructing a continuous approximation to the boundary data, here we present error estimates for both the velocity-pressure formulation and the pseudostress-velocity formulation of the two-dimensional Stokes driven cavity flow.


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Additional Information

Zhiqiang Cai
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Yanqiu Wang
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078

DOI: https://doi.org/10.1090/S0025-5718-08-02177-7
Received by editor(s): September 13, 2007
Received by editor(s) in revised form: May 7, 2008
Published electronically: October 1, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.