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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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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.