Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

作     者：Xuechun Liu Haijin Wang Jue Yan Xinghui Zhong Xuechun Liu;Haijin Wang;Jue Yan;Xinghui Zhong

作者机构：School of Mathematical SciencesZhejiang UniversityHangzhou310027ZhejiangChina School of ScienceNanjing University of Posts and TelecommunicationsNanjing210023JiangsuChina Department of MathematicsIowa State UniversityAmes50011IAUSA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2024年第6卷第1期

页      面：257-278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：supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214) the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011) supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716) supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347) 

主　　题：Direct discontinuous Galerkin(DDG)method with interface correction Symmetric DDG method Superconvergence Fourier analysis Eigen-structure 

摘      要：This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion *** apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical *** on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔ*** observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)*** experiments are provided to verify the theoretical results.