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

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 Ω of R³, 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 (Hs(Ω))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.