A virtual class of non-conforming finite elements and its applications to Poisson's equation

Abstract

In this paper, we develop and analyze the virtual class of nonconforming Finite Element inspired from the classical Crouzeix-Raviart element in two and three-dimensions. We focus on Poisson’s equation for theoretical and numerical results. We show that the discrete problem is stable and the a priori error estimates are optimal. Two numerical tests are presented to demonstrate the theoretical results.