Volume 55, Number 3, May-June 2021
|Page(s)||939 - 967|
|Published online||05 May 2021|
A generalized finite element method for problems with sign-changing coefficients
Inria Sophia Antipolis Méditerranée, 2004 Route des Lucioles, 06902 Valbonne, France
2 Laboratoire J.A. Dieudonné UMR CNRS 7351, Parc Valrose, 06108 Nice, France
3 Institut für Angewandte und Numerische Mathematik, Karlsruher Institut für Technologie (KIT), Englerstr. 2, D-76131 Karlsruhe, Germany
* Corresponding author: firstname.lastname@example.org
Accepted: 27 January 2021
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.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15 / 78A48 / 35J20
Key words: Generalized finite element method / multiscale method / sign-changing coefficients / T-coercivity
© EDP Sciences, SMAI 2021
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