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

## 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 |
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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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