Robust estimates for hp-adaptive approximations of non-self-adjoint eigenvalue problems
Please always quote using this URN:urn:nbn:de:0296-matheon-12105
- We present new residual estimates based on Kato's square root theorem for spectral approximations of diagonalizable non-self-adjoint differential operators of convection-diffusion-reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experiments demonstrate the efficiency and reliability of our approach.
Author: | Stefano Giani, Luka Grubišić, Agnieszka Międlar, Jeffrey S. Ovall |
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URN: | urn:nbn:de:0296-matheon-12105 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2013/05/06 |
Release Date: | 2013/05/06 |
Tag: | a posteriori error estimates; convection-diffusion-reaction operator; eigenvalue problem; finite element method; hp-adaptive mesh refinement; non-self-adjoint operator |
Institute: | Research Center Matheon |
Technische Universität Berlin | |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Preprint Number: | 1008 |