@Article{NMTMA-7-214,
author = {Tie Zhang and Jingna Liu},
title = {Accuracy Enhancement of Discontinuous Galerkin Method for Hyperbolic Systems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2014},
volume = {7},
number = {2},
pages = {214--233},
abstract = {<p style="text-align: justify;">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&#39; systems by using an upwind-like DG
method. We prove that the $L_2$-error of the DG solution is of
order $k+1/2$, and further the post-processed DG solution is of
order $2k+1$ if $Q_k$-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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.1216nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5872.html}
}