The Scott-Vogelius Method for the Stokes Problem on Anisotropic Meshes

Abstract

This paper analyzes the Scott-Vogelius divergence-free element pair on anisotropic meshes. We explore the behavior of the inf-sup stability constant with respect to the aspect ratio on meshes generated with a standard barycenter mesh refinement strategy, as well as a newly introduced incenter refinement strategy. Numerical experiments are presented which support the theoretical results.