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

doi:10.1080/00207160.2017.1335866

	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
	2018
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
卷号	95 期号:1 页码:114-143
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.
关键词	Multisymplectic formulation Hamiltonian PDEs local discontinuous Galerkin method numerical flux conservation law
DOI	10.1080/00207160.2017.1335866
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000428749300008
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29986
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.