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A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS
Ma, Chupeng1,2; Cao, Liqun1,2
2018
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume56Issue:1Pages:369-396
AbstractIn 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.
KeywordMaxwell-Schrodinger equations finite element method Crank-Nicolson scheme optimal error estimate
DOI10.1137/16M1085231
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
WOS IDWOS:000426741600016
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30016
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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