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We present reliable a-posteriori error estimates for $hp$-adaptive finiteelement approximations of eigenvalue/eigenvector problems. Starting from ourearlier work on $h$ adaptive finite element approximations we show a way toobtain reliable and efficient a-posteriori estimates in the $hp$-setting. Atthe core of our analysis is the reduction of the problem on the analysis of theassociated boundary value problem. We start from the analysis of Wohlmuth andMelenk and combine this with our a-posteriori estimation framework to obtaineigenvalue/eigenvector approximation bounds.

Reliable a-posteriori error estimators for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems