How to Design a Generic Accuracy-Enhancing Filter for Discontinuous Galerkin Methods  

作　　者：Xiaozhou Li 

机构地区：[1]School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,Sichuan,China

出　　处：《Communications on Applied Mathematics and Computation》2022年第3期759-782,共24页应用数学与计算数学学报（英文）

基　　金：Funding for this work was partially supported by the National Natural Science Foundation of China(NSFC)under Grant no.11801062.

摘　　要：Higher order accuracy is one of the well-known beneficial properties of the discontinu-ous Galerkin(DG)method.Furthermore,many studies have demonstrated the supercon-vergence property of the semi-discrete DG method.One can take advantage of this super-convergence property by post-processing techniques to enhance the accuracy of the DG solution.The smoothness-increasing accuracy-conserving(SIAC)filter is a popular post-processing technique introduced by Cockburn et al.(Math.Comput.72(242):577-606,2003).It can raise the convergence rate of the DG solution(with a polynomial of degree k)from order k+1 to order 2k+1 in the L2 norm.This paper first investigates general basis functions used to construct the SIAC filter for superconvergence extraction.The generic basis function framework relaxes the SIAC filter structure and provides flexibility for more intricate features,such as extra smoothness.Second,we study the distribution of the basis functions and propose a new SIAC filter called compact SIAC filter that significantly reduces the support size of the original SIAC filter while preserving(or even improving)its ability to enhance the accuracy of the DG solution.We prove the superconvergence error estimate of the new SIAC filters.Numerical results are presented to confirm the theoretical results and demonstrate the performance of the new SIAC filters.

关 键 词：Discontinuous Galerkin method SUPERCONVERGENCE Smoothness-increasing accuracy-conserving(SIAC)filter Convolution filtering POST-PROCESSING 

分 类 号：O17[理学—数学]