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Accuracy Enhancement of Discontinuous Galerkin Method for Hyperbolic Systems

Published online by Cambridge University Press:  28 May 2015

Tie Zhang  and
Jingna Liu
Tie Zhang*
Affiliation:
Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China
Jingna Liu
Affiliation:
Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China
*
Corresponding author.Email address:ztmath@163.com
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Abstract

We study the enhancement of accuracy, by means of the convolution post-processing technique, for discontinuous Galerkin(DG) approximations to hyperbolic problems. Previous investigations have focused on the superconvergence obtained by this technique for elliptic, time-dependent hyperbolic and convection-diffusion problems. In this paper, we demonstrate that it is possible to extend this post-processing technique to the hyperbolic problems written as the Friedrichs’ systems by using an upwind-like DG method. We prove that the L2-error of the DG solution is of order k+1/2, and further the post-processed DG solution is of order 2k+1 if Qk-polynomials are used. The key element of our analysis is to derive the (2k+1)-order negative norm error estimate. Numerical experiments are provided to illustrate the theoretical analysis.

Keywords

65N3065M60Discontinuous Galerkin methodhyperbolic problemaccuracy enhancementpost-processingnegative norm error estimate
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 2 , May 2014 , pp. 214 - 233
Copyright
Copyright © Global Science Press Limited 2014

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