1D Discontinuous Galerkin Methods for Hyperbolic Equations

Abstract

In Ch. 5 we described the implementation of the continuous Galerkin (CG) method for scalar hyperbolic equations. In this chapter we describe the implementation of the discontinuous Galerkin (DG) method. We show how this method can be used for the 1D wave equation which is representative of hyperbolic equations. We rely heavily on the theory that we have already presented in Ch. 3 on interpolation and in Ch. 4 on numerical integration. We only consider scalar equations in this chapter and extend the implementation of the DG method to systems of nonlinear partial differential equations in Ch. 7.