Citation for published item: qi niD F nd qru i § si¡ D vF nd wiedl rD eF nd yv llD tF @PHITA 9 o ust error estim tes for pproxim tions of nonEselfE djoint eigenv lue pro lemsF9D xumeris he w them tikFD IQQ @QAF ppF RUIERWSF Further information on publisher's website:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00211-015-0752-3.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract We present new residual estimates based on Kato's square root theorem for spectral approximations of non-self-adjoint differential operators of convection-diffusion-reaction type. It is not assumed that the eigenvalue/vector approximations are obtained from any particular numerical method, so these estimates may be applied quite broadly. Key eigenvalue and eigenvector error results are illustrated in the context of an hp-adaptive finite element algorithm for spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. The efficiency of these error estimates is also strongly suggested empirically.Keywords eigenvalue problems · non-self-adjoint operators · convection-diffusion-reaction operators · a posteriori error estimates · hp-adaptive finite elementsMathematics Subject Classification (2000) 65N30 · 65N25 · 65N15
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