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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1990-0995211-2
PII: S 0025-5718(1990)0995211-2
Keywords: Stokes problem, mixed finite elements, pointwise error estimates
Article copyright: © Copyright 1990 American Mathematical Society