An observation on Korn’s inequality for nonconforming finite element methods

Abstract

By utilizing a simple observation on traces of rigid motions we are able to strengthen a result of Brenner (2004) on Korn’s inequality for nonconforming finite element methods. The approach here is tightly connected to the theory developed in Brenner’s work. Our motivation for the analysis was the desire to show that a robust Darcy–Stokes element satisfies Korn’s inequality, and to achieve this the stronger result seems necessary.