ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE

	ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE
	Ma, Chupeng 1; Cao, Liqun2,3 ; Huang, Jizu2,3
	2019
发表期刊	INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN	1705-5105
卷号	16 期号:1 页码:139-166
摘要	In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell-Schrodinger system in the Coulomb gauge. We propose a fully discrete finite element scheme for the system and prove the conservation of energy and the stability estimates of the scheme. By approximating the vector potential A and the scalar potential phi respectively in two finite element spaces satisfying certain orthogonality relation, we tackle the mixed derivative term in the discrete system and make the numerical computations and the theoretical analysis more easier. The existence and uniqueness of solutions to the discrete system are also investigated. The (almost) unconditionally error estimates are derived for the numerical scheme without certain restriction like tau <= Ch(alpha) on the time step tau by using a new technique. Finally, numerical experiments are carried out to support our theoretical analysis.
关键词	Maxwell-Schrodinger finite element method energy conserving error estimates
语种	英语
资助项目	National Natural Science Foundation of China[11571353] ; National Natural Science Foundation of China[91330202] ; Funds for Creative Research Group of China[11321061]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000459444000007
出版者	ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32541
专题	计算数学与科学工程计算研究所
通讯作者	Ma, Chupeng
作者单位	1.Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Ma, Chupeng,Cao, Liqun,Huang, Jizu. ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2019,16(1):139-166.
APA	Ma, Chupeng,Cao, Liqun,&Huang, Jizu.(2019).ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,16(1),139-166.
MLA	Ma, Chupeng,et al."ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 16.1(2019):139-166.