Space-time discontinuous Galerkin method for parabolic problems in time-dependent domains

In this report a space-time discontinuous Galerkin (DG) finite element method for the solution of the advection-diffusion-reaction equation in time-dependent domains is presented and analyzed. The variational formulation is based on a combination of the space-time DG method developed by van der Vegt and van der Ven for hyperbolic partial differential equations and the DG algorithm for elliptic equations by Arnold, Brezzi, Cockburn and Marini.