Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor
Robust error estimates for approximations of non-self-adjoint eigenvalue problems
Giani, S.; Grubišić, L.; Międlar, A.; Ovall, J.
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. |
Public URL | https://durham-repository.worktribe.com/output/1426148 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-015-0752-3.
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