Numerical evaluation of a non-conforming discontinuous Galerkin method on triangular meshes for solving the time-domain Maxwell equations

We report on a detailed numerical evaluation of the non-dissipative, non-conforming discontinuous Galerkin (DG) method on triangular meshes, for solving the two-dimensional time-domain Maxwell equations. This DG method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a second order leap-frog time integration scheme. Moreover, non-conforming meshes with arbitrary-level hanging nodes are allowed. Here, our objective is to assess the convergence, the stability and the efficiency of the method, but also discuss its limitations, through numerical experiments for 2D propagation problems in homogeneous and heterogeneous media with various types and locations of material interfaces.