典型文献
Negative Norm Estimates for Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Nonlinear Hyperbolic Equations
文献摘要：
In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solu-tions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.
文献关键词：
中图分类号：
作者姓名：
Qi Tao;Yan Xu;Xiaozhou Li
作者机构：
Beijing Computational Science Research Center,Beijing 100193,China;School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China
文献出处：
引用格式：
[1]Qi Tao;Yan Xu;Xiaozhou Li-.Negative Norm Estimates for Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Nonlinear Hyperbolic Equations)[J].应用数学与计算数学学报,2022(01):250-270
A类：
SIAC,ficulties
B类：
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AB值：
0.511693
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