Course introduction

The 6 lectures course is addressed to practitioners of a standard Finite Element (FE) method familiar with basic variational formulations, (Bubnov-) Galerkin method and the standard technology of FEs. The class combines a short introduction to the Discontinuous Petrov-Galerkin (DPG) Method with Optimal Test Functions with a crash course on the energy spaces forming the exact sequence and the corresponding FE discretizations. We will introduce the participants to the parhp3D – a 3D MPI/openMP code supporting hp-discretizations of the exact sequence elements on hybrid (tets+cubes+prisms+pyramids) meshes and demonstrate how to implement the DPG method in such a framework.
On the application side we will focus on wave propagation problems: time-harmonic acoustics,
Maxwell equations, and elastodynamics.