An error estimate for two-dimensional Stokes driven cavity flow

Cai, Zhiqiang; Wang, Yanqiu

doi:10.1090/S0025-5718-08-02177-7

An error estimate for two-dimensional Stokes driven cavity flow
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by Zhiqiang Cai and Yanqiu Wang PDF

Math. Comp. 78 (2009), 771-787 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.

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