Space-time discontinuous Galerkin finite element methods

In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilization operators necessary to maintain stable and non-oscillatory solutions. In addition, a pseudo-time integration method for the solution of the algebraic equations resulting from the DG disctretization and the relation between the space-time DG method and an arbitrary lagrangian Eulerian approach are discussed. Finally, a brief overview of some applications to aerodynamics is given