In this report we analyze further the space-time discontinuous Galerkin (DG) finite element method for the solution of the advection-diffusion-reaction equation in time-dependent domains. We prove that the method is consistent, stable, coercive, and gives a unique solution. We also analyze the error estimates and $hp$-convergence of the method. The analysis is completed by analyzing the corresponding dual problems.
|Publisher||Department of Applied Mathematics, University of Twente|