Discontinuous Galerkin methods and fast iterative solvers for the numerical solution of compressible flow

This thesis deals with the numerical simulation of compressible laminar flow in two and three space dimensions. The discontinuous Galerkin method is employed for the high-order discretization of the governing equations, leading to large algebraic systems. The focus of this work lies in the development of efficient multilevel methods for the iterative solution of these equation systems. Here, the components of the solver are carefully chosen to match the characteristics of the model equations and the discretization scheme in terms of flexibility and robustness. Theoretical justifications prove the feasibility of the approach together with a number of numerical experiments.