Open Access
Issue
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
Page(s) 1185 - 1200
DOI https://doi.org/10.1051/m2an/2024033
Published online 27 June 2024
  1. J. An and Z. Zhang, An efficient spectral-Galerkin approximation and error analysis for Maxwell transmission eigenvalue problems in spherical geometries. J. Sci. Comput. 75 (2018) 157–181. [CrossRef] [MathSciNet] [Google Scholar]
  2. I. Babuška and J. Osborn, Eigenvalue problems. Handbook of Numerical Analysis. In Vol. II of Finite Element Methods (Part 1), edited by P.G. Ciarlet and J.L. Lions. Elseveier Science Publishers B.V., North-Holland (1991). [Google Scholar]
  3. F. Cakoni, D. Colton and H. Haddar, On the determination of Dirichlet or transmission eigenvalues from far field data. C. R. Math. 348 (2010) 379–383. [CrossRef] [Google Scholar]
  4. F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, 2nd edition. SIAM (2023). [Google Scholar]
  5. F. Cakoni, D. Colton, P. Monk and J. Sun, The inverse electromagnetic scattering problem for anisotropic media. Inverse Probl. 26 (2010) 074004. [CrossRef] [Google Scholar]
  6. F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium. Appl. Anal. 88 (2009) 475–493. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Camaño, R. Rodríguez and P. Venegas, Convergence of a lowest-order finite element method for the transmission eigenvalue problem. Calcolo 55 (2018) 1–14. [CrossRef] [MathSciNet] [Google Scholar]
  8. P.G. Ciarlet, The finite element method for elliptic problems. Classics in Applied Mathematics. SIAM, Philadelphia (2002) 40. [Google Scholar]
  9. D. Colton, P. Monk and J. Sun, Analytical and computational methods for transmission eigenvalues. Inverse Probl. 26 (2010) 045011. [CrossRef] [Google Scholar]
  10. R. Hiptmair, Finite elements in computational electromagnetism. Acta Numer. 11 (2002) 237–339. [CrossRef] [MathSciNet] [Google Scholar]
  11. T.-M. Huang, W.-Q. Huang and W.-W. Lin, A robust numerical algorithm for computing Maxwell’s transmission eigenvalue problems. SIAM J. Sci. Comput. 37 (2015) A2403–A2423. [Google Scholar]
  12. X. Ji, J. Sun and T. Turner, Algorithm 922: a mixed finite element method for Helmholtz transmission eigenvalues. ACM Trans. Math. Softw. 38 (2012) 29. [Google Scholar]
  13. A. Kleefeld, A numerical method to compute interior transmission eigenvalues. Inverse Probl. 29 (2013) 104012. [CrossRef] [Google Scholar]
  14. Q. Liu, T. Li and S. Zhang, A mixed element scheme for the Helmholtz transmission eigenvalue problem for anisotropic media. Inverse Probl. 39 (2023) 055005. [CrossRef] [Google Scholar]
  15. J. Meng, G. Wang and L. Mei, Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes. IMA J. Numer. Anal. 43 (2023) 1685–1717. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [CrossRef] [Google Scholar]
  17. P. Monk and J. Sun, Finite element methods for Maxwell’s transmission eigenvalues. SIAM J. Sci. Comput. 34 (2012) B247–B264. [CrossRef] [Google Scholar]
  18. D. Mora and I. Velásquez, A virtual element method for the transmission eigenvalue problem. Math. Models Methods Appl. Sci. 28 (2018) 2803–2831. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.-C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [Google Scholar]
  20. J.-C. Nédélec, A new family of mixed finite elements in R3. Numer. Math. 50 (1986) 57–81. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. P¨aiv¨arinta and J. Sylvester, Transmission eigenvalues. SIAM J. Math. Anal. 40 (2008) 738–753. [Google Scholar]
  22. J. Sun, Estimation of transmission eigenvalues and the index of refraction from Cauchy data. Inverse Probl. 27 (2010) 015009. [Google Scholar]
  23. J. Sun, Iterative methods for transmission eigenvalues. SIAM J. Numer. Anal. 49 (2011) 1860–1874. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Sun, A mixed FEM for the quad-curl eigenvalue problem. Numer. Math. 132 (2016) 185–200. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Sun and L. Xu, Computation of Maxwell’s transmission eigenvalues and its applications in inverse medium problems. Inverse Probl. 29 (2013) 104013. [CrossRef] [Google Scholar]
  26. J. Sun and A. Zhou, Finite Element Methods for Eigenvalue Problems. CRC Press, Boca Raton, FL (2017). [Google Scholar]
  27. C. Wang, Z. Sun and J. Cui, A new error analysis of a mixed finite element method for the quad-curl problem. Appl. Math. Comput. 349 (2019) 23–38. [MathSciNet] [Google Scholar]
  28. X. Wu and W. Chen, Error estimates of the finite element method for interior transmission problems. J. Sci. Comput. 57 (2013) 331–348. [CrossRef] [MathSciNet] [Google Scholar]
  29. Y. Yang, H. Bi, H. Li and J. Han, Mixed methods for the Helmholtz transmission eigenvalues. SIAM J. Sci. Comput. 38 (2016) A1383–A1403. [Google Scholar]

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