Introduction to Discontinuous Galerkin Methods

Abstract

The purpose of this chapter is to present an overview of the construction of discontinuous Galerkin finite element methods for a general class of second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic partial differential equations, ultra-parabolic equations, first-order hyperbolic problems, the Kolmogorov-Fokker-Planck equations of Brownian motion, the equations of boundary layer theory in hydrodynamics, and various other degenerate equations.