An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

doi:10.1007/s42967-025-00489-z

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (3): 1095-1114.doi: 10.1007/s42967-025-00489-z

An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

Jinhua Feng^1,2, Yanjun Li^2,3, Hai Bi², Yidu Yang²

1. School of Digital Humanities, Guizhou Normal University, Guiyang, 550025, Guizhou, China;
2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, Guizhou, China;
3. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, China

收稿日期:2024-05-22 修回日期:2024-09-13 出版日期:2026-06-20 发布日期:2026-05-29
通讯作者: Yidu Yang, Email: ydyang@gznu.edu.cn E-mail:ydyang@gznu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11561014, 11761022).

An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

Jinhua Feng^1,2, Yanjun Li^2,3, Hai Bi², Yidu Yang²

1. School of Digital Humanities, Guizhou Normal University, Guiyang, 550025, Guizhou, China;
2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, Guizhou, China;
3. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, China

Received:2024-05-22 Revised:2024-09-13 Online:2026-06-20 Published:2026-05-29
Contact: Yidu Yang, Email: ydyang@gznu.edu.cn E-mail:ydyang@gznu.edu.cn
Supported by:
This study was supported by The Hong Kong-Macau-Taiwan Science and Technology Cooperation Project of the Science and Technology Innovation Action Plan in Shanghai (No. 23510760200); Oriental Talent Youth Program of Shanghai (No. Y3DFRCZL01); Outstanding Program of the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. Y2023080), and Strategic Priority Research Program of the Chinese Academy of Sciences (Category A: No. Y3ZKXDZL04).

摘要/Abstract

摘要： In this paper, we study the a posteriori error estimates of the conforming mixed method for the modified transmission eigenvalue problem proposed by Cogar et al. (Inverse Problems 33: 055010, 2017). We give the a posteriori error estimator of the approximate eigenpair, prove the reliability and efficiency of the estimator for the approximate eigenfunction, and present the reliability of the estimator for the approximate eigenvalue. We also implement adaptive computation and exhibit the numerical experiments which show that the approximate eigenvalues obtained by the adaptive computation reach the optimal convergence order.

关键词: Modified transmission eigenvalues, Conforming mixed method, A priori error estimates, A posteriori error estimates, Absorbing media, Adaptive method

Abstract: In this paper, we study the a posteriori error estimates of the conforming mixed method for the modified transmission eigenvalue problem proposed by Cogar et al. (Inverse Problems 33: 055010, 2017). We give the a posteriori error estimator of the approximate eigenpair, prove the reliability and efficiency of the estimator for the approximate eigenfunction, and present the reliability of the estimator for the approximate eigenvalue. We also implement adaptive computation and exhibit the numerical experiments which show that the approximate eigenvalues obtained by the adaptive computation reach the optimal convergence order.

Key words: Modified transmission eigenvalues, Conforming mixed method, A priori error estimates, A posteriori error estimates, Absorbing media, Adaptive method

中图分类号:

65N25
65N30

Jinhua Feng, Yanjun Li, Hai Bi, Yidu Yang. An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 1095-1114.

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An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

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