In physics and computational engineering, numerical approximations of "real-world" problems play an important role. DG（Discontinuous Galerkin） methods form a subclass of the so called FEM（Finite Element Methods）that provide a very flexible (e.g. in terms of geometry) though precise way of numerical simulation tools.
In this work a highly precise novel type of DG-FEM that uses "physical" basis functions will be presented. As will be shown, high order time integration is an inherent property of the method, which makes highly convergent in the whole space time domain of interest.