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We propose an a posteriori error estimator for high-order $p$- or $hp$-finiteelement discretizations of selfadjoint linear elliptic eigenvalue problems thatis appropriate for estimating the error in the approximation of an eigenvaluecluster and the corresponding invariant subspace. The estimator is based on thecomputation of approximate error functions in a space that complements the onein which the approximate eigenvectors were computed. These error functions areused to construct estimates of collective measures of error, such as theHausdorff distance between the true and approximate clusters of eigenvalues,and the subspace gap between the corresponding true and approximate invariantsubspaces. Numerical experiments demonstrate the practical effectivity of theapproach.

A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques