A posteriori error analysis for nonconforming approximation of multiple eigenvalues

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix--Raviart non-conforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues.