Discontinuous element methods (DG and mortar)

Abstract

Up to now we have considered Galerkin methods with subspaces of continuous polynomial functions, either within the finite element method (Chapter 3) or the spectral element method (Chapter 10). This chapter deals with approximation techniques based on subspaces of polynomials that are discontinuous between elements. We will, in particular, introduce the so-called Discontinuous Galerkin method (DG) and the mortar method. We will carry out this for the Poisson problem first, and then generalize to the case of diffusion and transport problems (see Chapter 12). To maintain the presentation general we will consider a partition of the computational domain into disjoint subdomains that may be either finite or spectral elements.