The inf-sup stability of the lowest order Taylor-Hood pair on Anisotropic Meshes
Provides theoretical justification for using Taylor-Hood elements on anisotropic meshes, which is important for computational fluid dynamics simulations requiring local mesh refinement.
The authors prove uniform inf-sup (LBB) stability for the lowest order Taylor-Hood pairs on anisotropic meshes with refined edge and corner patches, enabling stable approximation of Stokes-type equations under anisotropic refinements.
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.