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Discontinuous Galerkin methods of the non-selfadjoint Steklov eigenvalue problem in inverse scattering

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  • Meng, Jian
  • Mei, Liquan

Abstract

In this paper, we apply discontinuous Galerkin methods to the non-selfadjoint Steklov eigenvalue problem arising in inverse scattering. The variational formulation of the problem is non-selfadjoint and does not satisfy H1-elliptic condition. By using the spectral approximation theory of compact operators, we prove the spectral approximation and optimal convergence order for the eigenvalues. Finally, some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex Steklov eigenvalues.

Suggested Citation

  • Meng, Jian & Mei, Liquan, 2020. "Discontinuous Galerkin methods of the non-selfadjoint Steklov eigenvalue problem in inverse scattering," Applied Mathematics and Computation, Elsevier, vol. 381(C).
  • Handle: RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302733
    DOI: 10.1016/j.amc.2020.125307
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    References listed on IDEAS

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    1. Fortin, A. & Yakoubi, D., 2019. "An adaptive discontinuous Galerkin method for very stiff systems of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 330-347.
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    Cited by:

    1. Feng, Jinhua & Wang, Shixi & Bi, Hai & Yang, Yidu, 2023. "An hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problem," Applied Mathematics and Computation, Elsevier, vol. 450(C).

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