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

doi:10.1080/00207160.2017.1335866

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs
	Cai, Wenjun 1; Sun, Yajuan2 ; Wang, Yushun 1; Zhang, Huai 3
刊名	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
	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
DOI	10.1080/00207160.2017.1335866
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
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000428749300008
内容类型	期刊论文
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.