full
search.png

Search

close.png

Cancel

arrow
Volume 15, Issue 1-2
Fully Computable Error Bounds for Eigenvalue Problem

Qichen Hong, Hehu Xie, Meiling Yue & Ning Zhang

Int. J. Numer. Anal. Mod., 15 (2018), pp. 260-276.

Published online: 2018-01

Preview Full PDF 2811 24307

Cited by

google scholar semantic scholar
Export citation
  • Abstract

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an asymptotically lower bound of the general eigenvalues. Furthermore, we also give a guaranteed upper bound of the error estimates for the first eigenfunction approximation and a guaranteed lower bound of the first eigenvalue based on computable error estimator. Some numerical examples are presented to validate the theoretical results deduced in this paper.

  • Keywords

Eigenvalue problem, computable error estimate, guaranteed upper bound, guaranteed lower bound, complementary method.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hongqichen@lsec.cc.ac.cn (Qichen Hong)

hhxie@lsec.cc.ac.cn (Hehu Xie)

yuemeiling@lsec.cc.ac.cn (Meiling Yue)

zhangning114@lsec.cc.ac.cn (Ning Zhang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-260, author = {Hong , QichenXie , HehuYue , Meiling and Zhang , Ning}, title = {Fully Computable Error Bounds for Eigenvalue Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {260--276}, abstract = {

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an asymptotically lower bound of the general eigenvalues. Furthermore, we also give a guaranteed upper bound of the error estimates for the first eigenfunction approximation and a guaranteed lower bound of the first eigenvalue based on computable error estimator. Some numerical examples are presented to validate the theoretical results deduced in this paper.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10567.html} }
TY - JOUR T1 - Fully Computable Error Bounds for Eigenvalue Problem AU - Hong , Qichen AU - Xie , Hehu AU - Yue , Meiling AU - Zhang , Ning JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 260 EP - 276 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10567.html KW - Eigenvalue problem, computable error estimate, guaranteed upper bound, guaranteed lower bound, complementary method. AB -

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an asymptotically lower bound of the general eigenvalues. Furthermore, we also give a guaranteed upper bound of the error estimates for the first eigenfunction approximation and a guaranteed lower bound of the first eigenvalue based on computable error estimator. Some numerical examples are presented to validate the theoretical results deduced in this paper.

Hong , QichenXie , HehuYue , Meiling and Zhang , Ning. (2018). Fully Computable Error Bounds for Eigenvalue Problem. International Journal of Numerical Analysis and Modeling. 15 (1-2). 260-276. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard