On the Discrete Friedrichs Inequality for Nonconforming Finite Elements

In this paper we establish the validity of the discrete Friedrichs inequality for piecewise linear Crouzeix-Raviart nonconforming finite elements in polygonal domains. It represents an extension of an important result proven for a polygonal convex domain to a general polygonal nonconvex domain. This result has applications in the analysis of exterior approximations of partial differential equations as, e.g., the Navier-Stokes equations and convection-diffusion problems.