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On the approximation of electromagnetic fields by edge finite elements. Part 4: analysis of the model with one sign-changing coefficient

Patrick Ciarlet 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In electromagnetism, in the presence of a negative material surrounded by a classical material, the electric permittivity, and possibly the magnetic permeability, can exhibit a sign-change at the interface. In this setting, the study of electromagnetic phenomena is a challenging topic. We focus on the time-harmonic Maxwell equations in a bounded set $\Omega$ of ${\mathbb R}^3$, and more precisely on the numerical approximation of the electromagnetic fields by edge finite elements. Special attention is paid to low-regularity solutions, in terms of the Sobolev scale $({\boldsymbol{H}}^{\mathtt{s}}(\Omega))_{\mathtt{s}>0}$. With the help of T-coercivity, we address the case of one sign-changing coefficient, both for the model itself, and for its discrete version. Optimal a priori error estimates are derived.
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https://hal.inria.fr/hal-03273264
Contributor : Patrick Ciarlet Connect in order to contact the contributor
Submitted on : Tuesday, June 29, 2021 - 9:55:28 AM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM
Long-term archiving on: : Thursday, September 30, 2021 - 6:15:01 PM

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Patrick Ciarlet. On the approximation of electromagnetic fields by edge finite elements. Part 4: analysis of the model with one sign-changing coefficient. 2021. ⟨hal-03273264⟩

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