This Wednesday (July 4, 2012) Jens Niegemann, Benedikt Oswald and me held a short course on Discontinuous Galerkin Methods as part of the 8th Workshop on Numerical Methods for Optical Nano Structures.
I covered the introduction (part I), Jens spoke about the DGM on tetrahedra and necessary extensions for performing simulations of realistic nano-structures including the implementation of dispersive media and Perfectly Matched Layers (PMLs). He also covered performance considerations and the implementation of the DGM on modern graphics processing units (GPUs) as well as improvements of the time integration (part II).
In part III, I discussed the DGM on irregular meshes (meshes containing hanging nodes) as well as adaptivity. The former is a prerequisite for performing unconstrained adaptive mesh refinement, specifically hp-adaptivity. All of the above is dealing with the DGM in time-domain.
In part IV, Benedikt moved on to frequency domain formulations and discussed the symmetric interior penalty DG method (SIP-DG).
The slides will soon be available on the workshop website. My own slides are also available here Part I and here Part III. Please note that the focus of the course is on explaining basic ideas rather than rigor.