The a Priori and a Posteriori Error Estimates for Modified Interior Transmission Eigenvalue Problem in Inverse Scattering
Year: 2023
Author: Yanjun Li, Yidu Yang, Hai Bi
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 503–529
Abstract
In this paper, we discuss the conforming finite element method for a modified interior transmission eigenvalues problem. We present a complete theoretical analysis for the method, including the a priori and a posteriori error estimates. The theoretical analysis is conducted under the assumption of low regularity on the solution. We 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. Finally, we report numerical experiments to show that our posteriori error estimator is effective and the approximations can reach the optimal convergence order. The numerical results also indicate that the conforming finite element eigenvalues approximate the exact ones from below, and there exists a monotonic relationship between the conforming finite element eigenvalues and the refractive index through numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0124
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 503–529
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Modified interior transmission eigenvalues a priori error estimates a posteriori error estimates adaptive algorithm.