A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS

doi:10.1137/16M1085231

	A CRANK-NICOLSON FINITE ELEMENT METHOD AND THE OPTIMAL ERROR ESTIMATES FOR THE MODIFIED TIME-DEPENDENT MAXWELL-SCHRODINGER EQUATIONS
	Ma, Chupeng 1,2; Cao, Liqun1,2
	2018
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	56 期号:1 页码:369-396
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.
关键词	Maxwell-Schrodinger equations finite element method Crank-Nicolson scheme optimal error estimate
DOI	10.1137/16M1085231
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
WOS记录号	WOS:000426741600016
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30016
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.