EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 3 (May-June 2021) ESAIM: M2AN, 55 3 (2021) 939-967 References
Free Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 939 - 967
DOI https://doi.org/10.1051/m2an/2021007
Published online 05 May 2021
  1. A. Abdulle, M.E. Huber and S. Lemaire, An optimization-based numerical method for diffusion problems with sign-changing coefficients. C. R. Math. Acad. Sci. Paris 355 (2017) 472–478. [CrossRef] [Google Scholar]
  2. A.-S. Bonnet-Ben Dhia, M. Dauge and K. Ramdani, Analyse spectrale et singularités d’un problème de transmission non coercif. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 717–720. [CrossRef] [Google Scholar]
  3. A.-S. Bonnet-Ben Dhia, P. Ciarlet Jr. and C.M. Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math. 234 (2010) 1912–1919. [CrossRef] [MathSciNet] [Google Scholar]
  4. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. Ciarlet Jr., T-coercivity for scalar interface problems between dielectrics and metamaterials. ESAIM: M2AN 46 (2012) 1363–1387. [CrossRef] [EDP Sciences] [Google Scholar]
  5. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. Ciarlet Jr., T-coercivity for the Maxwell problem with sign-changing coefficients. Comm. Part. Differ. Equ. 39 (2014) 1007–1031. [Google Scholar]
  6. A.-S. Bonnet-Ben Dhia, L. Chesnel and P. Ciarlet Jr., Two-dimensional Maxwell’s equations with sign-changing coefficients. Appl. Numer. Math. 79 (2014) 29–41. [Google Scholar]
  7. A.-S. Bonnet-Ben Dhia, C. Carvalho and P. Ciarlet Jr., Mesh requirements for the finite element approximation of problems with sign-changing coefficients. Numer. Math. 138 (2018) 801–838. [Google Scholar]
  8. E. Bonnetier, C. Dapogny and F. Triki, Homogenization of the eigenvalues of the Neumann-Poincaré operator. Arch. Ration. Mech. Anal. 234 (2019) 777–855. [Google Scholar]
  9. R. Bunoiu and K. Ramdani, Homogenization of materials with sign changing coefficients. Commun. Math. Sci. 14 (2016) 1137–1154. [Google Scholar]
  10. C. Carvalho, L. Chesnel and P. Ciarlet Jr., Eigenvalue problems with sign-changing coefficients. C. R. Math. Acad. Sci. Paris 355 (2017) 671–675. [Google Scholar]
  11. L. Chesnel and P. Ciarlet Jr., T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients. Numer. Math. 124 (2013) 1–29. [Google Scholar]
  12. E.T. Chung and P. Ciarlet Jr., A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials. J. Comput. Appl. Math. 239 (2013) 189–207. [Google Scholar]
  13. P.G. Ciarlet, The finite element method for elliptic problems. In: Vol. 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). [Google Scholar]
  14. P. Ciarlet Jr. and M. Vohralík, Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. ESAIM: M2AN 52 (2018) 2037–2064. [EDP Sciences] [Google Scholar]
  15. C. Engwer, P. Henning, A. Målqvist and D. Peterseim, Efficient implementation of the localized orthogonal decomposition method. Comput. Methods Appl. Mech. Eng. 350 (2019) 123–153. [Google Scholar]
  16. D. Gallistl and D. Peterseim, Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. Comput. Methods Appl. Mech. Eng. 295 (2015) 1–17. [Google Scholar]
  17. D. Gallistl and D. Peterseim, Computation of quasi-local effective diffusion tensors and connections to the mathematical theory of homogenization. Multiscale Model. Simul. 15 (2017) 1530–1552. [Google Scholar]
  18. F. Hellman and A. Målqvist, Contrast independent localization of multiscale problems. Multiscale Model. Simul. 15 (2017) 1325–1355. [Google Scholar]
  19. F. Hellman, A. Målqvist and S. Wang, Numerical upscaling for heterogeneous materials in fractured domains. ESAIM: M2AN 55 (2021) S761–S784. [EDP Sciences] [Google Scholar]
  20. P. Henning and D. Peterseim, Oversampling for the multiscale finite element method. Multiscale Model. Simul. 11 (2013) 1149–1175. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Kornhuber and H. Yserentant, Numerical homogenization of elliptic multiscale problems by subspace decomposition. Multiscale Model. Simul. 14 (2016) 1017–1036. [Google Scholar]
  22. R. Kornhuber, D. Peterseim and H. Yserentant, An analysis of a class of variational multiscale methods based on subspace decomposition. Math. Comput. 87 (2018) 2765–2774. [Google Scholar]
  23. J.J. Lee and S. Rhebergen, A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients. Preprint arXiv:1911.01984 (2019). [Google Scholar]
  24. R. Maier, Computational multiscale methods in unstructured heterogeneous media. Ph.D. thesis, Universität Augsburg (2020). [Google Scholar]
  25. A. Målqvist and D. Peterseim, Localization of elliptic multiscale problems. Math. Comput. 83 (2014) 2583–2603. [Google Scholar]
  26. S. Nicaise and J. Venel, A posteriori error estimates for a finite element approximation of transmission problems with sign changing coeficients. J. Comput. Appl. Math. 235 (2011) 4272–4282. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85 (2000) 3966–3969. [CrossRef] [PubMed] [Google Scholar]
  28. D. Peterseim, Variational multiscale stabilization and the exponential decay of fine-scale correctors. In: Vol. 114 of Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lect. Notes Comput. Sci. Eng. Springer, Cham (2016) 341–367. [Google Scholar]
  29. D. Peterseim, Eliminating the pollution effect in Helmholtz problems by local subscale correction. Math. Comput. 86 (2017) 1005–1036. [Google Scholar]
  30. D. Peterseim and R. Scheichl, Robust numerical upscaling of elliptic multiscale problems at high contrast. Comput. Methods Appl. Math. 16 (2016) 579–603. [Google Scholar]
  31. D. Peterseim and B. Verfürth, Computational high frequency scattering from high contrast media. Math. Comput. 89 (2020) 2649–2674. [Google Scholar]
  32. D. Peterseim, D. Varga and B. Verfürth, From domain decomposition to homogenization theory. Domain Decomposition Methods in Science and Engineering XXV. In: Vol. 138 of Lect. Notes Comp. Sci. Eng. Springer, Cham (2020) 29–40. [Google Scholar]
  33. D.R. Smith, J.B. Pendry and M.C.K. Wiltshire, Metamaterials and negative refractive index. Science 305 (2004) 788–792. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you