The inf-sup stability of the lowest order Taylor-Hood pair on Anisotropic Meshes

Abstract

Uniform LBB conditions are desirable to approximate the solution of Navier-Stokes, Oseen, and Stokes equations on anisotropic meshes and to enable anisotropic refinements. We prove such conditions for the second order Taylor-Hood pairs ${\mathbb{Q}}_2\times {\mathbb{Q}}_1$ and ${\mathbb{P}}_2\times {\mathbb{P}}_1$ on a class of anisotropic meshes. These meshes may contain refined edge and corner patches. To this end, we generalise Verfürth's trick and recent results by some of the authors.

18 pages, 12 figures