Implementation of the Galerkin discontinous method in the DGM software package

The mathematical foundations of the discontinuous Galerkin method are presented, on which the implementation of the DGM software package is based. This software package implements a modal approach to the Galerkin method with discontinuous basis functions for solving the Navier-Stokes equations on grids of arbitrary structure. Particular attention is paid to the implementation of the Cockburn limiter for cells of arbitrary shape.