On pressure estimates for the Navier-Stokes equations

Abstract

This paper presents a simple, general technique to prove finite element method (FEM) pressure stability and convergence. Typically, pressure estimates are ignored in the literature. However, full reliability of a numerical method is not established unless the solution pair $(u,p)$ is treated. The simplicity of the proposed technique puts pressure estimates within reach of many existing and future numerical methods and lends itself to the numerical analyst's toolbox.