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Robust error estimates for approximations of non-self-adjoint eigenvalue problems

Giani, S.; Grubišić, L.; Międlar, A.; Ovall, J.

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Authors

L. Grubišić

A. Międlar

J. Ovall



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.

Citation

Giani, S., Grubišić, L., Międlar, A., & Ovall, J. (2016). Robust error estimates for approximations of non-self-adjoint eigenvalue problems. Numerische Mathematik, 133(3), 471-495. https://doi.org/10.1007/s00211-015-0752-3

Journal Article Type Article
Acceptance Date Jun 1, 2015
Online Publication Date Jul 9, 2015
Publication Date Jul 1, 2016
Deposit Date Jun 22, 2015
Publicly Available Date Jul 9, 2016
Journal Numerische Mathematik
Print ISSN 0029-599X
Electronic ISSN 0945-3245
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 133
Issue 3
Pages 471-495
DOI https://doi.org/10.1007/s00211-015-0752-3
Keywords 65N30, 65N25, 65N15.

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