A posterior error estimator and lower bound of a nonconforming finite element method

In this paper, we present an a posteriori error estimator and the lower bound for a nonconforming finite element approximation, i.e. the extended Crouzeix–Raviart element, of the Laplace eigenvalue problem. Under the guideline of the analysis to the Laplace source problem, we first give out an error indicator and prove it as the global upper and local lower bounds of the approximation error. We also give the lower-bound analysis for this type of nonconforming element on the adaptive meshes. Some numerical experiments are presented to verify our theoretical results.