Maximum Norm Error Estimates of Crouzeix-Raviart Nonconforming Finite Element Approximation of Navier-Stokes Problem

Abstract

This paper deals with Crouzeix-Raviart nonconforming finite element approximation of Navier-Stokes equation in a plane bounded domain, by using the so-called velocity-pressure mixed formulation. The quasi-optimal maximum norm error estimates of the velocity and its first derivatives and of the pressure are derived for nonconforming C-R scheme of stationary Navier-Stokes problem. The analysis is based on the weighted inf-sup condition and the technique of weighted Sobolev norm. By the way, the optimal $L^2$-error estimate for nonconforming finite element approximation is obtained.