The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. 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 calculations 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.

翻译：本文旨在研究连续与离散设置下，导电介质中随时间变化的电场麦克斯韦方程组解的存在性、稳定性与收敛性。所考虑的情形代表一个物理问题：某子区域浸没在具有恒定介电常数与电导率函数的均匀介质中。众所周知，在这些均匀区域内，麦克斯韦方程组的解同样满足波动方程，这使得计算效率极高。因此，我们的问题可视为一个耦合问题，并据此推导稳定性与收敛性分析。多项数值算例验证了所提出的稳定显式有限元方案的理论收敛阶。