A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations

In this article, we carry out a systematic stability analysis for the explicit Runge–Kutta scheme coupled with a discontinuous Galerkin discretization in space for solving the time‐dependent Maxwell's equations. Many so‐called RKDG methods have been developed and successfully solved Maxwell's equations. However, to our best knowledge, there are quite limited rigorous analyses of RKDG methods devoted to Maxwell's equations. This paper is our initial effort in filling this gap by establishing the stability analysis for the RKDG methods of order two, three, and four. Numerical results consistent with our analysis are presented for the 3‐D Maxwell's equations.