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ANALYSIS OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MAXWELL-SCHRODINGER SYSTEM IN THE COULOMB GAUGE
Ma, Chupeng1; Cao, Liqun2,3; Huang, Jizu2,3
2019
Source PublicationINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN1705-5105
Volume16Issue:1Pages:139-166
AbstractIn 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.
KeywordMaxwell-Schrodinger finite element method energy conserving error estimates
Language英语
Funding ProjectNational Natural Science Foundation of China[11571353] ; National Natural Science Foundation of China[91330202] ; Funds for Creative Research Group of China[11321061]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000459444000007
PublisherISCI-INST SCIENTIFIC COMPUTING & INFORMATION
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32541
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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