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

TL;DR

This paper analyzes the stability, well-posedness, and convergence of a stabilized finite element scheme for time-dependent Maxwell's equations in conductive media, with validation through numerical examples.

Contribution

It introduces a stabilized explicit finite element method for Maxwell's equations in conductive media and provides rigorous stability and convergence analysis.

Findings

Numerical examples confirm theoretical convergence rates.

The scheme is stable and well-posed in both continuous and discrete settings.

The method effectively models Maxwell's equations in heterogeneous media.

Abstract

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.