Analysis of the convergence behavior of the static localized nonlinear approximation for a problem in electromagnetism

A study of the convergence behavior of the static localized nonlinear approximation (SLN) introduced by Habashy et al. (J. Geophys. Res. 98 (1993) 1759) is furnished for a specific case of the time-harmonic Maxwell equations. Some asymptotics are used to explain the robustness of this scheme in the high-conductivity case.