A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS
文献类型：期刊论文
| 作者 | Ma, Chupeng1,2; Cao, Liqun1,2
|
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2018 |
| 卷号 | 56期号:1页码:369-396 |
| 关键词 | Maxwell-Schrodinger equations finite element method Crank-Nicolson scheme optimal error estimate |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/16M1085231 |
| 英文摘要 | In this paper, we study a Crank-Nicolson finite element method for the modified Maxwell-Schrodinger equations, which are deduced from the time-dependent Maxwell-Schrodinger equations under some assumptions. We present an (almost) unconditionally optimal error estimate for the numerical algorithm which only requires the time step Delta t < 1. The key to our analysis is twofold. For one thing, we use some tricks to tackle the tough nonlinear terms without applying the inverse inequality to estimate the L-infinity norm of the numerical solutions and get rid of certain restrictions like Delta t <= C h(alpha) on the time step. For another, we employ a new technique to weaken the time step restriction required by the application of the discrete Gronwall inequality. Numerical tests are carried out to verify the theoretical results. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000426741600016 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/30015]  |
| 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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.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. A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2018,56(1):369-396. |
| APA | Ma, Chupeng,&Cao, Liqun.(2018).A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,56(1),369-396. |
| MLA | Ma, Chupeng,et al."A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 56.1(2018):369-396. |
入库方式： OAI收割
来源：数学与系统科学研究院
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