A time-domain solver is developed using a method from computational fluid dynamics to solve numerically the time-dependent 2D Maxwell system. The time-domain solver is based on a mixed finite-volume/finite-element method using a third-order accurate upwind scheme, and a three-stage explicit Runge-Kutta scheme is applied to the time integration. This results in a high-order-accurate scheme in both the time and the spatial variables.
Some questions, such as the treatment of the divergence-free-conditions and also the capture of the Maxwell solutions in the frequency domain, are discussed and some solutions are proposed. Numerical experiments are presented and the computed solutions are compared with the analytical ones or with the corresponding integral equation method solutions.