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

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.

Domaines: Analyse numérique [math.NA]

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-03273264v1⟩