Introduction -- Part I: Analysis of the discontinuous Galerkin method -- DGM for elliptic problems -- Methods based on a mixed formulation -- DGM for convection-diffusion problems -- Space-time discretization by multi-step methods -- Space-time discontinuous Galerkin method  -- Generalization of the DGM -- Part II:  Applications of the discontinuous Galerkin method -- Inviscid compressible flow -- Viscous compressible flow -- Fluid-structure interaction -- References -- Index.  .

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.