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Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods

Ainsworth, M. (2004) Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Journal of Computational Physics, 198 (1). pp. 106-130. ISSN 0021-9991

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Abstract

The dispersive and dissipative properties of hp version discontinuous Galerkin finite element approximation are studied in three different limits. For the small wave-number limit hk→0, we show the discontinuous Galerkin gives a higher order of accuracy than the standard Galerkin procedure, thereby confirming the conjectures of Hu and Atkins [J. Comput. Phys. 182 (2) (2002) 516]. If the mesh is fixed and the order p is increased, it is shown that the dissipation and dispersion errors decay at a super-exponential rate when the order p is much larger than hk. Finally, if the order is chosen so that 2p+1≈κhk for some fixed constant κ>1, then it is shown that an exponential rate of decay is obtained.

Item type: Article
ID code: 2163
Keywords: discrete dispersion relation, high wave number, discontinuous Galerkin approximation, hp-finite element method, computational physics, Mathematics, Physics
Subjects: Science > Mathematics
Science > Physics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 14 Dec 2006
    Last modified: 12 Mar 2012 10:37
    URI: http://strathprints.strath.ac.uk/id/eprint/2163

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