A non-conforming discontinuous Galerkin method for solving Maxwell's equations

This paper reviews the main features of a high-order non-dissipative discontinuous Galerkin (DG) method recently investigated in [H. Fahs, Int. J. Numer. Anal. Model., 6, 193-216, 2009] 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.