Taylor-Hood Finite Elements Research Articles

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

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.