In this talk, we will discuss the general properties of the DG-FEM formulation and try to place it into the context of alternative methods such as finite difference, finite volume, and finite element methods. The aim of this discussion will be to understand whether these basic properties suggest that this formulation is well suited as a generic tool for solving partial differential equations arising in computational science and engineering.
We will place particular emphasis on understanding central issues of flexibility, efficiency, and robustness and we will illustrate the performance of the formulation with examples taken from electromagnetics, plasma physics, gas dynamics, and free surface flows. We shall conclude the talk with a few open questions and suggestions for future work.