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Volume 7, Issue 3
Computable Error Estimates for a Nonsymmetric Eigenvalue Problem

Hehu Xie, Manting Xie, Xiaobo Yin & Meiling Yue

DOI: 10.4208/eajam.140317.250517a

East Asian J. Appl. Math., 7 (2017), pp. 583-602.

Published online: 2018-02

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  • Abstract

We provide some computable error estimates in solving a nonsymmetric eigenvalue problem by general conforming finite element methods on general meshes. Based on the complementary method, we first give computable error estimates for both the original eigenfunctions and the corresponding adjoint eigenfunctions, and then we introduce a generalised Rayleigh quotient to deduce a computable error estimate for the eigenvalue approximations. Some numerical examples are presented to illustrate our theoretical results.

  • Keywords

Nonsymmetric eigenvalue problem, computable error estimates, asymptotical exactness, finite element method, complementary method.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-583, author = {Hehu Xie, Manting Xie, Xiaobo Yin and Meiling Yue}, title = {Computable Error Estimates for a Nonsymmetric Eigenvalue Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {583--602}, abstract = {

We provide some computable error estimates in solving a nonsymmetric eigenvalue problem by general conforming finite element methods on general meshes. Based on the complementary method, we first give computable error estimates for both the original eigenfunctions and the corresponding adjoint eigenfunctions, and then we introduce a generalised Rayleigh quotient to deduce a computable error estimate for the eigenvalue approximations. Some numerical examples are presented to illustrate our theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.140317.250517a}, url = {http://global-sci.org/intro/article_detail/eajam/10766.html} }
TY - JOUR T1 - Computable Error Estimates for a Nonsymmetric Eigenvalue Problem AU - Hehu Xie, Manting Xie, Xiaobo Yin & Meiling Yue JO - East Asian Journal on Applied Mathematics VL - 3 SP - 583 EP - 602 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.140317.250517a UR - https://global-sci.org/intro/article_detail/eajam/10766.html KW - Nonsymmetric eigenvalue problem, computable error estimates, asymptotical exactness, finite element method, complementary method. AB -

We provide some computable error estimates in solving a nonsymmetric eigenvalue problem by general conforming finite element methods on general meshes. Based on the complementary method, we first give computable error estimates for both the original eigenfunctions and the corresponding adjoint eigenfunctions, and then we introduce a generalised Rayleigh quotient to deduce a computable error estimate for the eigenvalue approximations. Some numerical examples are presented to illustrate our theoretical results.

Hehu Xie, Manting Xie, Xiaobo Yin and Meiling Yue. (2018). Computable Error Estimates for a Nonsymmetric Eigenvalue Problem. East Asian Journal on Applied Mathematics. 7 (3). 583-602. doi:10.4208/eajam.140317.250517a
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