English

Fortin Operator for the Taylor-Hood Element

Numerical Analysis 2021-12-21 v1 Numerical Analysis

Abstract

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 P2P_2-P0P_0 and the augmented Taylor-Hood element in 3D.

Cite

@article{arxiv.2104.13953,
  title  = {Fortin Operator for the Taylor-Hood Element},
  author = {Lars Diening and Johannes Storn and Tabea Tscherpel},
  journal= {arXiv preprint arXiv:2104.13953},
  year   = {2021}
}

Comments

14 pages

R2 v1 2026-06-24T01:36:39.557Z