TY - GEN A1 - Miedlar, Agnieszka T1 - Functional perturbation results and the balanced AFEM algorithm for self-adjoint PDE eigenvalue problems N2 - We introduce functional perturbation results for PDE eigenvalue problems including the functional backward error and the functional condition number. These results are used to establish a combined a posteriori error estimator embodying the discretization and the approximation error for the simple eigenpair. Based on known perturbation results in $H^{1}(\Omega)$ and $H^{-1}(\Omega)$ norms and a standard residual a posteriori error estimator, a balancing AFEM algorithm is proposed. The stopping criterion for the eigensolver is based on the equilibrating strategy, i.e., iterations proceed as long as the discrete part of the error estimator dominates the continuous part. All our statements are illustrated with several numerical examples. KW - functional backward error KW - functional condition number KW - self-adjoint eigenvalue problem KW - adaptive finite element method (AFEM) KW - balanced AFEM algorithm Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/897 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8978 ER -