We will consider evolutionary systems, i.e. time-dependent systems coming from modeling physical problems as first-order systems. Examples are wave-equation, heat-equation, Maxwell's-equations and many more. We will look especially into problems, where the type of the underlying PDE changes depending on the part of the domain considered and prove convergence of a numerical method based on a discontinuous Galerkin method in time and standard FEM in space.

Dr. Sebastian Franz obtained his PhD in Mathematics at the University of Technology Dresden, Germany, in 2008 and completed his Habilitation in 2014 also at the University of Technology Dresden, both on topics of singularly perturbed partial differential equations. He has been a post-doc at the University of Limerick in Ireland from 2009-2011 under supervision of Dr. Natalia Kopteva working on a-posteriori error estimation for singularly perturbed problems. Currently he is working as an assistant professor/lecturer equivalent at the University of Technology in Dresden. Recently his focus has shifted to time-dependent problems and the class of evolutionary problems.