KMS Of Academy of mathematics and systems sciences, CAS
| 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
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| 2019 | |
| Source Publication | INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
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| ISSN | 1705-5105 |
| Volume | 16Issue:1Pages:139-166 |
| Abstract | 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. |
| Keyword | Maxwell-Schrodinger finite element method energy conserving error estimates |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11571353] ; National Natural Science Foundation of China[91330202] ; Funds for Creative Research Group of China[11321061] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000459444000007 |
| Publisher | ISCI-INST SCIENTIFIC COMPUTING & INFORMATION |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32541 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Ma, Chupeng |
| Affiliation | 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 |
| 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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