A space-time discontinuous Galerkin discretization for the linear transport equation

We consider a full-upwind DG approximation in space and time for the linear transport equation. Based on our results for linear symmetric Friedrichs systems we establish inf-sup stability and convergence in a mesh-dependent DG norm, and we construct an error indicator with respect to this norm. Numerical results of test problems with known solution demonstrate the efficiency of the a priori and a posteriori results as well for smooth and for non-smooth solutions. Then, we show that by introducing suitable degrees of freedom on the space-time element boundaries the corresponding hybrid formulation yields a reduction to a considerably smaller linear system.