Space-time Discontinuous Galerkin Method For Advection-diffusion Problems On Time-dependent Domains

It is studied that Space-time discontinuous Galerkin (DG) finite element method of the advection-diffusion equation on time-dependent domains. In the space-time DG discretization no distinction is made between the space and time variables and discontinuous basis functions are used both in space and time. This approach results in an efficient numerical technique for moving and deforming elements, is suitable for parallel computation. A complete derivation of the space-time DG method for the advection-diffusion equation is given ,using F.Brezzi's flux,together with the relation of the space-time discretization with the arbitrary Lagrangian Eulerian (ALE) approach. Detailed proofs of stability and error estimates are also given.