Cockburn, Bernardo and Luskin, Mitchell and Shu, ChiWang and Suli, Endre (2001) Enhanced accuracy by postprocessing 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 postprocessing technique, for finite element approximations to transient hyperbolic equations. The postprocessing 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 postprocessed 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 postprocessed 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) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1248 
Deposited By:  Lotti Ekert 
Deposited On:  21 May 2011 16:08 
Last Modified:  29 May 2015 18:56 
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