TY - JOUR
T1 - Accuracy Enhancement of Discontinuous Galerkin Method for Hyperbolic Systems
AU - Tie Zhang & Jingna Liu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 214
EP - 233
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1216nm
UR - https://global-sci.org/intro/article_detail/nmtma/5872.html
KW - Discontinuous Galerkin method, hyperbolic problem, accuracy enhancement, post-processing, negative norm error estimate.
AB - <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>