Fortin Operator for the Taylor-Hood Element

04/28/2021

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by   Lars Diening, et al.

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We design a Fortin operator for the lowest-order Taylor-Hood element in any dimension, which was previously constructed only in 2D. In the construction we use tangential edge bubble functions for the divergence correcting operator. This naturally leads to an alternative inf-sup stable reduced finite element pair. Furthermore, we provide a counterexample to the inf-sup stability and hence to existence of a Fortin operator for the P_2-P_0 and the augmented Taylor-Hood element in 3D.