Publication details for Dr Stefano GianiGiani, 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.
- Publication type: Journal Article
- ISSN/ISBN: 0029-599X, 0945-3245
- DOI: 10.1007/s00211-015-0752-3
- Keywords: 65N30, 65N25, 65N15.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.