典型文献
How to Design a Generic Accuracy-Enhancing Filter for Discontinuous Galerkin Methods
文献摘要：
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 theo-retical results and demonstrate the performance of the new SIAC filters.
文献关键词：
中图分类号：
作者姓名：
Xiaozhou Li
作者机构：
School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,Sichuan,China
文献出处：
引用格式：
[1]Xiaozhou Li-.How to Design a Generic Accuracy-Enhancing Filter for Discontinuous Galerkin Methods)[J].应用数学与计算数学学报,2022(03):759-782
A类：
SIAC,Cockburn,Comput
B类：
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AB值：
0.523787
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