Space-time Discrete DG Method For Solving Maxwell’s Equations In Metamaterials

With the rapid development of meta-materials in recent years, scientists become more and more interested in the study of them. In this paper we main-ly focus on the numerical methods for solving a typical model-Drude model, which describes the propagation of electromagnetic waves in meta-materials. Inspired by the work in [22,23], we adopt space-time discrete discontinuous Galerkin method for the Maxwell system composed of four differential equa-tions. Both the L2 stability and error estimate are verified, i.e., the L2 error rate in time is O(τr+1) and the L2 error rate in space is O(hk+1/2). Moreover, the numerical examples in 2D and 3D validate the theoretical results. Actual-ly, the numerical results show that the L2 error rate in space is O(hk+1), which is better than the theoretical prediction. Further, the numerical tests in 2D demonstrate that the numerical flux in time at nodes superconverges at a rate O(τ2t+1).Further, we prove that the CG-DG scheme proposed in [23] for solving Maxwell equations in dispersive media is convergent.