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Volume 38, Issue 4
The Shifted-Inverse Power Weak Galerkin Method for Eigenvalue Problems

Qilong Zhai, Xiaozhe Hu & Ran Zhang

DOI: 10.4208/jcm.1903-m2018-0101

J. Comp. Math., 38 (2020), pp. 606-623.

Published online: 2020-04

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  • Abstract

This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions. Numerical examples are presented to validate the theoretical analysis.

  • Keywords

weak Galerkin finite element method, eigenvalue problem, shifted-inverse power method, lower bound.

  • AMS Subject Headings

65N30, 65N15, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhaiql@pku.edu.cn (Qilong Zhai)

xiaozhe.hu@tufts.edu (Xiaozhe Hu)

zhangran@jlu.edu.cn (Ran Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-606, author = {Zhai , QilongHu , Xiaozhe and Zhang , Ran}, title = {The Shifted-Inverse Power Weak Galerkin Method for Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {4}, pages = {606--623}, abstract = {

This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions. Numerical examples are presented to validate the theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1903-m2018-0101}, url = {http://global-sci.org/intro/article_detail/jcm/16465.html} }
TY - JOUR T1 - The Shifted-Inverse Power Weak Galerkin Method for Eigenvalue Problems AU - Zhai , Qilong AU - Hu , Xiaozhe AU - Zhang , Ran JO - Journal of Computational Mathematics VL - 4 SP - 606 EP - 623 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1903-m2018-0101 UR - https://global-sci.org/intro/article_detail/jcm/16465.html KW - weak Galerkin finite element method, eigenvalue problem, shifted-inverse power method, lower bound. AB -

This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions. Numerical examples are presented to validate the theoretical analysis.

Zhai , QilongHu , Xiaozhe and Zhang , Ran. (2020). The Shifted-Inverse Power Weak Galerkin Method for Eigenvalue Problems. Journal of Computational Mathematics. 38 (4). 606-623. doi:10.4208/jcm.1903-m2018-0101
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