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A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems

  • Liang Wang
  • Chunguang XiongEmail author
  • Huibin Wu
  • Fusheng Luo
Article
  • 15 Downloads

Abstract

In this paper, we express and analyze mixed discontinuous Galerkin(DG) methods of biharmonic eigenvalue problems as well as present the error analysis for them. The analysis consists of two parts. First, we propose a residual-based a posteriori error estimator in the approximate eigenfunctions and eigenvalues. The error in the eigenfunctions is measured both in the L2 and DG (energy-like) norms. In addition, we prove that if the error estimator converges to zero, then the distance of the computed eigenfunction from the true eigenspace also converges to zero, and so, the computed eigenvalue converges to a true eigenvalue. Next, we establish an a priori error estimate with the optimal convergence order both in the L2 and DG norms. We show that the methods can retain the same convergence properties they enjoy in the case of source problems.

Keywords

Biharmonic eigenvalue problems DGFEM A priori error estimate A posteriori error estimate 

Mathematics Subject Classification (2010)

65F10 65N30 65N55 

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Authors and Affiliations

  1. 1.Department of MathematicsBeijing Institute of TechnologyBeijingChina
  2. 2.Third Institute of OceanographyState Oceanic AdministrationSiming DistrictChina

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