Discontinuous galerkin methods for time-dependent convection dominated problems: Basics, recent developments and comparison with other methods

Abstract

In this survey article, we will give a short summary of the basic algorithm issues of discontinuousGalerkin methods for time-dependent convection dominated problems. We will then give a few representative examples of recent developments of discontinuous Galerkin methods for such problems, and provide comparisons with several other types of numerical methods commonly used for similar or related problems. For the comparison, we concentrate mainly on the methods presented in the London Mathematical Society EPSRC Durham Symposium on Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations.