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

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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 (http://dx.doi.org/10.1016/j.jcp.2004.01.004)

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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.

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