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Journal of Scientific Computing

, Volume 79, Issue 2, pp 914–934 | Cite as

Acceleration of Weak Galerkin Methods for the Laplacian Eigenvalue Problem

  • Qilong Zhai
  • Hehu XieEmail author
  • Ran Zhang
  • Zhimin Zhang
Article
  • 33 Downloads

Abstract

Recently, we proposed a weak Galerkin finite element method for the Laplace eigenvalue problem. In this paper, we present two-grid and two-space skills to accelerate the weak Galerkin method. By choosing parameters properly, the two-grid and two-space weak Galerkin method not only doubles the convergence rate, but also maintains the asymptotic lower bounds property of the weak Galerkin method. Some numerical examples are provided to validate our theoretical analysis.

Keywords

Weak Galerkin finite element method Eigenvalue problem Two-grid method Two-space method Lower bound 

Mathematics Subject Classification

Primary 65N30 65N15 65N12 74N20 Secondary 35B45 35J50 35J35 

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Authors and Affiliations

  1. 1.Department of MathematicsJilin UniversityChangchunPeople’s Republic of China
  2. 2.LSEC, ICMSEC, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China
  4. 4.Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of EducationJilin UniversityChangchunPeople’s Republic of China
  5. 5.Beijing Computational Science Research CenterBeijingPeople’s Republic of China
  6. 6.Department of MathematicsWayne State UniversityDetroitUSA

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