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Article
Robust Error Estimates for Approximations of Non-Self-Adjoint Eigenvalue Problems
Numerische Mathematik
  • Stefano Giani, Durham University
  • Luka Grubišić, University of Zagreb
  • Agnieszka Międlar, Technische Universität Berlin
  • Jeffrey S. Ovall, Portland State University
Document Type
Citation
Publication Date
7-1-2016
Disciplines
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.

DOI
10.1007/s00211-015-0752-3
Persistent Identifier
http://archives.pdx.edu/ds/psu/18920
Citation Information
Giani, S., Grubišić, L., Międlar, A. et al. Robust Error Estimates for Approximations of Non-Self-Adjoint Eigenvalue Problems. Numerische Mathematik. (2016) 133 (3): 471-495.