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A generalized finite element method for problems with sign-changing coefficients

Théophile Chaumont-Frelet 1, 2 Barbara Verfürth 3
1 ATLANTIS - Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné
2 LJAD
JAD - Laboratoire Jean Alexandre Dieudonné
Abstract : Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal Decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features. We derive optimal linear convergence in the energy norm independently of the potentially low regularity of the exact solution. Numerical experiments illustrate the theoretical convergence rates and show the applicability of the method for a large class of sign-changing diffusion problems.
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https://hal.inria.fr/hal-02496832
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Submitted on : Thursday, August 27, 2020 - 8:44:17 PM
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  • HAL Id : hal-02496832, version 2
  • ARXIV : 2002.10818

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Théophile Chaumont-Frelet, Barbara Verfürth. A generalized finite element method for problems with sign-changing coefficients. 2020. ⟨hal-02496832v2⟩

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