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A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement (CROSBI ID 178665)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Bank, Randolph E. ; Grubišić, Luka ; Ovall, Jeffrey A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement // Applied numerical mathematics, 66 (2013), 1-29. doi: 10.1016/j.apnum.2012.11.004

Podaci o odgovornosti

Bank, Randolph E. ; Grubišić, Luka ; Ovall, Jeffrey

engleski

A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement

We present a general framework for the a posteriori estimation and enhancement of error in eigenvalue/eigenvector computations for symmetric and elliptic eigenvalue problems, and provide detailed analysis of a specific and important example within this framework--finite element methods with continuous, affine elements. A distinguishing feature of the proposed approach is that it provides provably efficient and reliable error estimation under very realistic assumptions, not only for single, simple eigenvalues, but also for clusters which may contain degenerate eigenvalues. We reduce the study of the eigenvalue/eigenvector error estimators to the study of associated boundary value problems, and make use of the wealth of knowledge available for such problems. Our choice of a posteriori error estimator, computed using hierarchical bases, very naturally offers a means not only for estimating error in eigenvalue/eigenvector computations, but also cheaply accelerating the convergence of these computations--sometimes with convergence rates which are nearly twice that of the unaccelerated approximations.

adaptive finite element methods ; convergence enhancement ; error estimation

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Podaci o izdanju

66

2013.

1-29

objavljeno

0168-9274

1873-5460

10.1016/j.apnum.2012.11.004

Povezanost rada

Matematika

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