Identifier: 2008-8
Author(s): C.-W. Shu
Title: Discontinuous Galerkin Methods: General Approach and Stability
Page count: 44 pp.
Abstract:
In these lectures, we will give a general introduction to the discontinuous Galerkin (DG) methods for solving time dependent, convection dominated partial differential equations (PDEs), including the hyperbolic conservation laws, convection diffusion equations, and PDEs containing higher order spatial derivatives such as the KdV equations and other nonlinear dispersive wave equations. We will discuss cell en- tropy inequalities, nonlinear stability, and error estimates. The important ingredient of the design of DG schemes, namely the adequate choice of numerical fluxes, will be explained in detail. Issues related to the implementation of the DG method will also be addressed.
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