Discontinuous Galerkin methods with transient hp-adaptation

The Discontinuous Galerkin (DG) method for Maxwell´s equations and dedicated techniques for adaptive mesh refinement are presented. The DG method offers two refinement mechanisms: the manipulation of the local mesh step size (h-adaptation) and the adaptation of the local approximation order (p-adaptation). For both cases, a new, optimal approximation after adaptation is obtained by means of projections between finite element spaces. Such projections as well as an estimator for the local smoothness of the solution are presented, which allow for performing transient mesh refinement, i.e., the continuous adaptation of the mesh according to the current situation.