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The aim of this article is to investigate the well-posedness, stability andconvergence of solutions to the time-dependent Maxwell's equations for electricfield in conductive media in continuous and discrete settings. The situation weconsider would represent a physical problem where a subdomain is emerged in ahomogeneous medium, characterized by constant dielectric permittivity andconductivity functions. It is well known that in these homogeneous regions thesolution to the Maxwell's equations also solves the wave equation which makescalculations very efficient. In this way our problem can be considered as acoupling problem for which we derive stability and convergence analysis. Anumber of numerical examples validate theoretical convergence rates of theproposed stabilized explicit finite element scheme.

Energy norm error estimates and convergence analysis for a stabilized Maxwell's equations in conductive media