A posteriori error analysis for nonconforming approximation of multiple eigenvalues
For researchers in numerical analysis, this provides theoretical justification for using a known error estimator in the practically relevant case of multiple eigenvalues.
The paper proves that an existing a posteriori error estimator for nonconforming finite element approximation of Laplace eigenvalues remains robust for multiple eigenvalues, with numerical examples confirming adaptive algorithm convergence.
In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, 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.