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

Durán, Ricardo G.; Nochetto, Ricardo H.

doi:10.1090/S0025-5718-1990-0995211-2

Weighted inf-sup condition and pointwise error estimates for the Stokes problem
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by Ricardo G. Durán and Ricardo H. Nochetto PDF

Math. Comp. 54 (1990), 63-79 Request permission

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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