On the approximation of electromagnetic fields by edge finite elements. Part 4: analysis of the model with one sign-changing coefficient - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Numerische Mathematik Year : 2022

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

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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Dates and versions

hal-03273264 , version 1 (29-06-2021)
hal-03273264 , version 2 (01-09-2022)
hal-03273264 , version 3 (14-09-2022)

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Cite

Patrick Ciarlet. On the approximation of electromagnetic fields by edge finite elements. Part 4: analysis of the model with one sign-changing coefficient. Numerische Mathematik, 2022, 152, pp.223-257. ⟨10.1007/s00211-022-01315-x⟩. ⟨hal-03273264v3⟩
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