Analysis of 2D Maxwell's Equations in a Time-Harmonic Regime

Abstract

The variational formulation is an essential tool to analyze the existence and uniqueness of the solution of certain partial differential equations with boundary conditions. We can further approximate this analytical solution by computing a corresponding numerical solution obtained by the finite element method. In this paper, we studied 2D Maxwell's equations in a time-harmonic regime. We established a corresponding variational formulation and proved its well-posedness in certain conditions. We also constructed a corresponding internal approximation and gave an error estimate within some prior assumptions. This theoretical analysis provides a basis to compute the numerical solution of time-harmonic 2D Maxwell's equations and gives physical significance to the transverse magnetic problem.