Repository: Freie Universität Berlin, Math Department

Discontinuous Galerkin methods

Cockburn, B. (2003) Discontinuous Galerkin methods. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 83 (11). 731 -754.

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This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience.We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block-diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another consequence of the use of discontinuous approximations is that these methods can easily handle irregular meshes with hanging nodes and approximations that have polynomials of different degrees in different elements. They are thus ideal for use with adaptive algorithms. Moreover, the methods are locally conservative (a property highly valued by the computational fluid dynamics community) and, in spite of providing discontinuous approximations, stable, and high-order accurate. Even more, when applied to non-linear hyperbolic problems, the discontinuous Galerkin methods are able to capture highly complex solutions presenting discontinuities with high resolution. In this paper, we concentrate on the exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems.

Item Type:Article
Additional Information:Plenary lecture presented at the 80th Annual GAMM Conference, Augsburg, 25–28 March 2002
Uncontrolled Keywords:discontinuous Galerkin methods, finite element methods
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:767
Deposited By: Ulrike Eickers
Deposited On:21 Sep 2009 13:42
Last Modified:21 Sep 2009 14:49

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