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Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs
Cai, Wenjun1; Sun, Yajuan2; Wang, Yushun1; Zhang, Huai3
2018
Source PublicationINTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN0020-7160
Volume95Issue:1Pages:114-143
AbstractThis 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.
KeywordMultisymplectic formulation Hamiltonian PDEs local discontinuous Galerkin method numerical flux conservation law
DOI10.1080/00207160.2017.1335866
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000428749300008
PublisherTAYLOR & FRANCIS LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29986
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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