In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary-level hanging nodes. The method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities. Numerical experiments with high-order elements show the potential of the method. © 2009 Elsevier B.V. All rights reserved.
Fahs, H., & Lanteri, S. (2010). A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics. Journal of Computational and Applied Mathematics, 234(4), 1088–1096. https://doi.org/10.1016/j.cam.2009.05.015