An error estimate for two-dimensional Stokes driven cavity flow
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- by Zhiqiang Cai and Yanqiu Wang;
- Math. Comp. 78 (2009), 771-787
- DOI: https://doi.org/10.1090/S0025-5718-08-02177-7
- Published electronically: October 1, 2008
- PDF | Request permission
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.References
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Bibliographic Information
- Zhiqiang Cai
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 235961
- Yanqiu Wang
- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- MR Author ID: 670715
- Received by editor(s): September 13, 2007
- Received by editor(s) in revised form: May 7, 2008
- Published electronically: October 1, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 78 (2009), 771-787
- MSC (2000): Primary 65N15, 65N30, 76D07
- DOI: https://doi.org/10.1090/S0025-5718-08-02177-7
- MathSciNet review: 2476559