Summary: We present an overview of the evolution of discontinuous Galerkin methods since their introduction by W. H. Reed and T. R. Hill [Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory (1973)], in the framework of neutron transport, until their most recent developments. We show how these methods made their way into the main stream of computational fluid dynamics, and how they are quickly finding use in a wide variety of applications. We review theoretical and algorithmic aspects of these methods as well as their applications to equations including nonlinear conservation laws, compressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.
For the entire collection see [Zbl 0935.00043].