Accuracy Enhancement of Discontinuous Galerkin Method for Hyperbolic Systems

作     者：Tie Zhang Jingna Liu 

作者机构：Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process IndustriesNortheastern UniversityShenyang 110004China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2014年第7卷第2期

页      面：214-233页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the State Key Laboratory of Synthetical Automation for Process Industries Fundamental Research Funds 2013ZCX02 the National Natural Science Funds of China 11371081 

主　　题：Discontinuous Galerkin method hyperbolic problem accuracy enhancement postprocessing negative norm error estimate 

摘      要：We study the enhancement of accuracy,by means of the convolution postprocessing technique,for discontinuous Galerkin(DG)approximations to hyperbolic *** investigations have focused on the superconvergence obtained by this technique for elliptic,time-dependent hyperbolic and convection-diffusion *** this paper,we demonstrate that it is possible to extend this postprocessing technique to the hyperbolic problems written as the Friedrichs’systems by using an upwind-like DG *** 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 Qkpolynomials are *** key element of our analysis is to derive the(2k+1)-order negative norm error *** experiments are provided to illustrate the theoretical analysis.