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Weighted inf-sup condition and pointwise error estimates for the Stokes problem

Authors: Ricardo G. Durán and Ricardo H. Nochetto
Journal: Math. Comp. 54 (1990), 63-79
MSC: Primary 65N30; Secondary 65N15, 76-08, 76D07
MathSciNet review: 995211
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Abstract: Convergence of mixed finite element approximations to the Stokes problem in the primitive variables is examined in maximum norm. Quasioptimal pointwise error estimates are derived for discrete spaces satisfying a weighted inf-sup condition similar to the Babuška -Brezzi condition. The usual techniques employed to prove the inf-sup condition in energy norm can be easily extended to the present situation, thus providing several examples to our abstract framework. The popular Taylor-Hood finite element is the most relevant one.

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Keywords: Stokes problem, mixed finite elements, pointwise error estimates
Article copyright: © Copyright 1990 American Mathematical Society