TY - JOUR T1 - Accuracy Enhancement of Discontinuous Galerkin Method for Hyperbolic Systems 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 -

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 $L_2$-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.