| 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 | |
Solving numerically the two-dimensional time harmonic Maxwell problem with sign-changing coefficients
1
Inria, 75013 Paris, France
2
CERMICS, ENPC, 77420 Champs-sur-Marne, France
3
POEMS, CNRS, INRIA, ENSTA, IPP. 91120 Palaiseau, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
23
January
2025
Accepted:
31
March
2026
Abstract
We are investigating the numerical solution to the 2D time-harmonic Maxwell equations in the presence of a classical medium and a metamaterial, that is with sign-changing coefficients. As soon as the problem has a (unique) solution, we are able to build a converging numerical approximation based on the finite element method, for which there is no constraint on the meshes related to the sign-changing behavior. To that aim, we use Lagrange finite elements to approximate the scalar potentials appearing in the Helmholtz decomposition of the vector-valued electromagnetic fields. Convergence in strong norm is proven for the fields. Numerical examples illustrate the theory.
Mathematics Subject Classification: 65J10 / 65N15 / 65N30 / 49J20
Key words: Maxwell’s equations / metamaterial / sign-changing coefficients / optimal control
© The authors. Published by EDP Sciences, SMAI 2026
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