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All issues Volume 60 / No 3 (May-June 2026) ESAIM: M2AN, 60 3 (2026) 1327-1362 References
Open Access
Issue
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
Page(s) 1327 - 1362
DOI https://doi.org/10.1051/m2an/2026032
Published online 01 June 2026
  1. A. Abdulle and S. Lemaire, An optimization-based method for sign-changing elliptic PDEs. Math. Mod. Num. Anal. 58 (2024) 2187–2223. [Google Scholar]
  2. A. Abdulle, M.E. Huber and S. Lemaire, An optimization-based numerical method for diffusion problems with sign-changing coefficients. C. R. Acad. Sci. Paris, Ser. 1 355 (2017) 472–478. [Google Scholar]
  3. F. Assous, P. CiarletJr. and S. Labrunie, Mathematical Foundations of Computational Electromagnetism, in Vol. 198 of Applied Mathematical Sciences. Springer, Berlin (2018). [Google Scholar]
  4. A.-S. Bonnet-Ben Dhia, P. CiarletJr. and C.M. Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math. 234 (2010) 1912–1919. Corrigendum p. 2616. [CrossRef] [MathSciNet] [Google Scholar]
  5. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. CiarletJr., T-coercivity for scalar interface problems between dielectrics and metamaterials. Math. Mod. Num. Anal. 46 (2012) 1363–1387. [CrossRef] [EDP Sciences] [Google Scholar]
  6. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. CiarletJr., T-coercivity for the Maxwell problem with sign-changing coefficients. Commun. Partial Differ. Equ. 39 (2014) 1007–1031. [CrossRef] [Google Scholar]
  7. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. CiarletJr., Two-dimensional Maxwell’s equations with sign-changing coefficients. Appl. Numer. Math. 79 (2014) 29–41. [Google Scholar]
  8. A.-S. Bonnet-Ben Dhia, C. Carvalho and P. CiarletJr., Mesh requirements for the finite element approximation of problems with sign-changing coefficients. Numer. Math. 138 (2018) 801–838. [Google Scholar]
  9. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, Springer (2011). [Google Scholar]
  10. E. Burman, A. Ern and J. Preuss, A hybridized Nitsche method for sign-changing elliptic PDEs. Math. Models Methods Appl. Sci. 35 (2025) 2977–3009. [Google Scholar]
  11. C. Carvalho, L. Chesnel and P. CiarletJr., Eigenvalue problems with sign-changing coefficients. C. R. Acad. Sci. Paris, Ser. I 355 (2017) 671–675. [Google Scholar]
  12. C. Carvalho, P. CiarletJr. and C. Scheid, Limiting amplitude principle and resonances in plasmonic structures with corners: numerical investigation. Comput. Methods Appl. Mech. Eng. 388 (2022) 114207. [Google Scholar]
  13. F. Chaaban, Unconditionally stable numerical methods for solving transmission problems with sign-changing coefficients. Ph.D. thesis, Institut Polytechnique de Paris (2025). [Google Scholar]
  14. G. Chavent, Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-by-Step Guide for Applications. Springer Science & Business Media (2010). [Google Scholar]
  15. L. Chesnel and P. CiarletJr., T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients. Numer. Math. 124 (2013) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. CiarletJr., On the approximation of electromagnetic fields by edge finite elements – Part 4: analysis of the model with one sign-changing coefficient. Numer. Math. 152 (2022) 223–257. [Google Scholar]
  17. P. CiarletJr., T-coercivity: a practical tool for the study of variational formulations in Hilbert spaces. Technical Report hal-05421231v1, HAL (2025). [Google Scholar]
  18. P. CiarletJr. and M. Vohralik, Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. Math. Model. Numer. Anal. 52 (2018) 2037–2064. [Google Scholar]
  19. P. Ciarlet Jr., D. Lassounon and M. Rihani, An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients. SIAM J. Numer. Anal. 61 (2023) 1316–1339. [Google Scholar]
  20. A. Ern and J.-L. Guermond, Finite Elements I: Approximation and Interpolation. Springer, Berlin (2021). [Google Scholar]
  21. B. Fabrèges, L. Gouarin and B. Maury, A smooth extension method. C. R. Math. 351 (2013) 361–366. [Google Scholar]
  22. V. Girault and P.A. Raviart, Finite Element Methods for Navier–Stokes Equations, in Vol. 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1986). [Google Scholar]
  23. P. Grisvard, Singularities in Boundary Value Problems, Vol. 22. Springer, Berlin (1992). [Google Scholar]
  24. M. Halla, Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility. Numer. Math. 148 (2021) 387–407. [Google Scholar]
  25. M. Halla, On the approximation of dispersive electromagnetic eigenvalue problems in two dimensions. IMA J. Numer. Anal. 43 (2023) 535–559. [Google Scholar]
  26. M. Halla, T. Hohage and F. Oberender, A new numerical method for scalar eigenvalue problems in heterogeneous, dispersive, sign-changing materials. J. Sci. Comput. 106 (2026). [Google Scholar]
  27. D.S. Jerison and C.E. Kenig, The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. 4 (2017 [1981]) 203–207. [Google Scholar]
  28. A. Kirsch and F. Hettlich, Mathematical theory of time-harmonic Maxwell’s equations. Springer, Berlin (2016). [Google Scholar]
  29. V. Kozlov, V.G. Mazia and J. Rossmann, Spectral Problems Associated With Corner Singularities of Solutions to Elliptic Equations, in Vol. 85 of Mathematical Surveys and Monographs. AMS (2001). [Google Scholar]
  30. D. Maystre and S. Enoch, Perfect lenses made with left-handed materials: Alice’s mirror? JOSA A 21 (2004) 122–131. [Google Scholar]
  31. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [Google Scholar]
  32. S. Nicaise and J. Venel, A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients. J. Comput. Appl. Math. 235 (2011) 4272–4282. [Google Scholar]
  33. J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85 (2000) 3966. [CrossRef] [Google Scholar]
  34. J.B. Pendry, D. Schurig and D.R. Smith, Controlling electromagnetic fields. Science 312 (2006) 1780–1782. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  35. S.A. Ramakrishna, Physics of negative refractive index materials. Rep. Prog. Phys. 68 (2005) 449–521. [CrossRef] [Google Scholar]
  36. D.R. Smith, J.B. Pendry and M.C.K. Wiltshire, Metamaterials and negative refractive index. Science 305 (2004) 788–792. [Google Scholar]

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