Conservation Properties of the Discontinuous Galerkin Method for Maxwell Equations

We investigate the conservation properties of the centered DO formulation for Maxwell equations. In particular, we state the problem and derive the criteria for charge conservation. It is shown that the centered scheme guarantees strict charge conservation for Cartesian discretizations with tensor product basis functions of arbitrary order. On unstructured grids, however, the conservation of charge is inherently violated. The reasons for this are of purely topological nature.