Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract

Lilienthal, Martin

Non-dissipative space time hp-discontinuous Galerkin method for the time-dependent Maxwell equations

A space-time finite element method for the time-dependent Maxwell equations is presented. The method allows for local hp-refinement in space and time by employing a space-time Galerkin approach and is thus well suited for hp-adaptivity. Inspired by the so called continuous Galerkin methods for ODEs, nonequal test and trial spaces are employed in the temporal direction. Combined with a (centered) discontinuous Galerkin approach in the spatial directions, a stable non-dissipative method is obtained. Numerical experiments in (3 1)D indicate that the method is suitable for space-time $hp$-adaptivity on dynamic discretizations.