A high order discontinuous Galerkin method for the Boltzmann Equation Gerhard Kitzler1 Joachim Sch oberl2 The Boltzmann equation is a statistical model for gases. The density distribution function f(t; x; v) describes the propability to nd a particle at time t near the spatial position x and which has the velocity close to v. The time evolution of f is given by the Boltzmann equation. The collision of particles is formulated in terms of the collision operator Q(f) which is local in x and t. We perform a Petrov-Galerkin method in the spatial domain and velocity domain R3. In the v domain the solution is expanded as a sum over multivariate Lagrange polynomials lj(x) times an appropriate gaussian peak. In space we discretize by a high order discontinuous Galerkin method with natural upwind uxes. Due to this expansion, the Boltzmann transport operator decouples when using Gau - Hermite integration rules of appropriate order into transport operators for the individual components. 1