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An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities

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Abstract

The elastic transmission eigenvalue problem, arising from the inverse scattering theory, plays a critical role in the qualitative reconstruction methods for elastic media. This paper proposes and analyzes an a posteriori error estimator of the finite element method for solving the elastic transmission eigenvalue problem with different elastic tensors and different mass densities in \(\mathbb {R}^{d}~(d=2,3)\). An adaptive algorithm based on the a posteriori error estimators is designed. Numerical results are provided to illustrate the efficiency of our adaptive algorithm.

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Acknowledgements

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

Funding

The work was supported by the National Natural Science Foundation of China (Grant Nos. 12261024, 11561014, 11761022).

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Authors and Affiliations

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

    Shixi Wang, Hai Bi & Yidu Yang

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  1. Shixi Wang
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  2. Hai Bi
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Correspondence to Yidu Yang.

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Wang, S., Bi, H. & Yang, Y. An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities. Adv Comput Math 50, 8 (2024). https://doi.org/10.1007/s10444-023-10099-z

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