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

Abstract

The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.