Cockburn, Bernardo and Luskin, Mitchell and Shu, Chi-Wang and Suli, Endre (2001) *Enhanced accuracy by post-processing for finite element methods for hyperbolic equations.* Technical Report. Mathematics of Computation. (Submitted)

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## Abstract

We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of only. For example, when polynomials of degree are used in the discontinuous Galerkin (DG) method, and the exact solution is globally smooth, the DG method is of order in the norm, whereas the post-processed approximation is of order ; if the exact solution is in only, in which case no order of convergence is available for the DG method, the post-processed approximation converges with order in where is a subdomain over which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.

Item Type: | Technical Report (Technical Report) |
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Subjects: | H - N > Numerical analysis |

Research Groups: | Numerical Analysis Group |

ID Code: | 1248 |

Deposited By: | Lotti Ekert |

Deposited On: | 21 May 2011 17:08 |

Last Modified: | 21 May 2011 17:08 |

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