Enhanced accuracy by post-processing for finite element methods for hyperbolic equations |
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Authors: | Bernardo Cockburn Mitchell Luskin Chi-Wang Shu Endre Sü li |
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Institution: | School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ; School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ; Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 ; Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom |
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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. |
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Keywords: | Post-processing finite element methods hyperbolic problems |
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