Mathematical and numerical analyses for the div-curl and div-curlcurl problems with a sign-changing coefficient - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2021

Mathematical and numerical analyses for the div-curl and div-curlcurl problems with a sign-changing coefficient

Abstract

We study the numerical approximation by edge finite elements of fields whose divergence and curl, or divergence and curl-curl, are prescribed in a bounded set $\Omega$ of $\mathbb{R}^3$, together with a boundary condition. Special attention is paid to solutions with low-regularity, in terms of the Sobolev scale $({\mathbf H}^{s}(\Omega))_{s>0}$. Among others, we consider an electromagnetic-like model including an interface between a classical medium and a metamaterial. In this setting the electric permittivity, and possibly the magnetic permeability, exhibit a sign-change at the interface. With the help of T-coercivity, we address the case of a model with one sign-changing coefficient, both for the model itself, and for its discrete version. Optimal error estimates are derived. Thanks to these results, we are also able to analyze the classical time-harmonic Maxwell equations, with one sign-changing coefficient.
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Dates and versions

hal-02567484 , version 1 (07-05-2020)
hal-02567484 , version 2 (10-02-2021)

Identifiers

  • HAL Id : hal-02567484 , version 2

Cite

Patrick Ciarlet. Mathematical and numerical analyses for the div-curl and div-curlcurl problems with a sign-changing coefficient. 2021. ⟨hal-02567484v2⟩
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