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Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs

文献类型：期刊论文

作者Cai, Wenjun1; Sun, Yajuan2; Wang, Yushun1; Zhang, Huai3
刊名INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
出版日期2018
卷号95期号:1页码:114-143
关键词Multisymplectic formulation Hamiltonian PDEs local discontinuous Galerkin method numerical flux conservation law
ISSN号0020-7160
DOI10.1080/00207160.2017.1335866
英文摘要This paper examines the novel local discontinuous Galerkin (LDG) discretization for Hamiltonian PDEs based on its multisymplectic formulation. This new kind of LDG discretizations possess one major advantage over other standard LDG method, which, through specially chosen numerical fluxes, states the preservation of discrete conservation laws (i.e. energy), and also the multisymplectic structure while the symplectic time integration is adopted. Moreover, the corresponding local multisymplectic conservation law holds at the units of elements instead of each node. Taking the nonlinear Schrodinger equation and the KdV equation as the examples, we illustrate the derivations of discrete conservation laws and the corresponding numerical fluxes. Numerical experiments by using the modified LDG method are demonstrated for the sake of validating our theoretical results.
资助项目National Basic Research Program of China[2014 CB845906] ; ITER-China Program[2014GB124005] ; National Natural Science Foundation of China[41274103] ; National Natural Science Foundation of China[11271195] ; National Natural Science Foundation of China[11321061] ; National Natural Science Foundation of China[11271357] ; National Natural Science Foundation of China[41504078]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000428749300008
出版者TAYLOR & FRANCIS LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/29985]  
专题计算数学与科学工程计算研究所
通讯作者Cai, Wenjun; Zhang, Huai
作者单位1.Nanjing Normal Univ, Sch Math Sci, Jiangsu Prov Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing, Peoples R China
3.Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714		 Cai, Wenjun,Sun, Yajuan,Wang, Yushun,et al. Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2018,95(1):114-143.
APA Cai, Wenjun,Sun, Yajuan,Wang, Yushun,&Zhang, Huai.(2018).Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,95(1),114-143.
MLA Cai, Wenjun,et al."Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 95.1(2018):114-143.

入库方式： OAI收割

来源：数学与系统科学研究院

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