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The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering

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Abstract

In this paper, we study the discontinuous Galerkin finite element method for the Steklov eigenvalue problem arising in inverse scattering. We present a complete error estimates including the a refined priori error estimate and the a posteriori error estimate, and prove the reliability and efficiency of the a posteriori error estimators for eigenfunctions up to higher order terms, and we also analyze the reliability of estimators for eigenvalues. Moreover, we carry out the numerical experiments in adaptive fashion which together with theoretical analysis show that our method reach the optimal convergence order.

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Acknowledgements

We cordially thank the editor and the referees for their valuable comments and suggestions which led to the improvement of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Yanjun Li, Hai Bi & Yidu Yang

  2. School of Big Data Applications and Economics, Guizhou University of Finance and Economics, Guiyang, 550001, China

    Yanjun Li

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  1. Yanjun Li
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Correspondence to Yidu Yang.

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Projects supported by the National Natural Science Foundation of China (Grant Nos. 11761022, 11561014), the Scientific Research Foundation of Guizhou University of Finance and Economics (No. 2020XYB10), and the Science and Technology Foundation of Guizhou Province (No. ZK[2021]012)

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Li, Y., Bi, H. & Yang, Y. The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering. J Sci Comput 91, 20 (2022). https://doi.org/10.1007/s10915-022-01787-x

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  • DOI: https://doi.org/10.1007/s10915-022-01787-x

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