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Journal of Computational Mathematics ›› 2020, Vol. 38 ›› Issue (4): 606-623.DOI: 10.4208/jcm.1903-m2018-0101

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THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS

Qilong Zhai1, Xiaozhe Hu2, Ran Zhang3   

  1. 1. Department of Mathematics, Peking University, Beijing 100871, China;
    2. Department of Mathematics, Tufts University, Medford, 02155, USA;
    3. Department of Mathematics, Jilin University, Changchun 130012, China
  • Received:2018-05-24 Revised:2018-10-12 Online:2020-07-15 Published:2020-07-15
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Qilong Zhai, Xiaozhe Hu, Ran Zhang. THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS[J]. Journal of Computational Mathematics, 2020, 38(4): 606-623.

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.
Key words: Weak Galerkin finite element method, Eigenvalue problem, Shifted-inverse power method, Lower bound

CLC Number: 

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