南方科技大学知识苑(SUSTech KC): H<SUP>1</SUP>-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION

Title	H¹-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION
Author	Quan, Chaoyu1,2 ; Wu, Xu3,4
Corresponding Author	Quan, Chaoyu
Publication Years	2023
DOI	10.1137/22M1506468
Source Title	SIAM JOURNAL ON NUMERICAL ANALYSIS Impact Factor & Quartile
ISSN	0036-1429
EISSN	1095-7170
Volume	61 Issue:5
Abstract	This work establishes H-1-norm stability and convergence for an L2 method on general nonuniform meshes when applied to the subdiffusion equation. Under mild constraints on the time step ratio rho(k), such as 0.4573328 <= rho(k) <= 3.5615528 for k >= 2, the positive semidefiniteness of a crucial bilinear form associated with the L2 fractional-derivative operator is proved. This result enables us to derive long time H-1-stability of L2 schemes. These positive semidefiniteness and H-1-stability properties hold for standard graded meshes with grading parameter 1 < r <= 3.2016538. In addition, error analysis in the H-1-norm for general nonuniform meshes is provided, and convergence of order (5 - alpha)/2 in the H-1-norm is proved for modified graded meshes when r > 5/alpha - 1. To the best of our knowledge, this study is the first work on H-1-norm stability and convergence of L2 methods on general nonuniform meshes for the subdiffusion equation.
Keywords	L2-type method subdiffusion equation graded mesh positive semidefiniteness H1-norm stability and convergence
URL	[Source Record]
Indexed By	SCI
Language	English
SUSTech Authorship	Corresponding
Funding Project	National Natural Sci-ence Foundation of China[12271241] ; Guangdong Basic and Applied Basic Research Foundation[2023B1515020030] ; Shenzhen Science and Technology Program[RCYX20210609104358076]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS Accession No	WOS:001082987300005
Publisher	SIAM PUBLICATIONS
ESI Research Field	MATHEMATICS
Data Source	Web of Science
Citation statistics
Document Type	Journal Article
Identifier	http://kc.sustech.edu.cn/handle/2SGJ60CL/582843
Department	Southern University of Science and Technology 理学院_数学系
Affiliation	1.Chinese Univ Hong Kong, Sch Sci & Engn, Shenzhen 518172, Guangdong, Peoples R China 2.Southern Univ Sci & Technol, SUS Tech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China 3.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China 4.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
First Author Affilication	Southern University of Science and Technology
Corresponding Author Affilication	Southern University of Science and Technology
Recommended Citation GB/T 7714	Quan, Chaoyu,Wu, Xu. H¹-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2023,61(5).
APA	Quan, Chaoyu,&Wu, Xu.(2023).H¹-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION.SIAM JOURNAL ON NUMERICAL ANALYSIS,61(5).
MLA	Quan, Chaoyu,et al."H¹-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION".SIAM JOURNAL ON NUMERICAL ANALYSIS 61.5(2023).

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H1-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION

H¹-NORM STABILITY AND CONVERGENCE OF AN L2-TYPE METHOD ON NONUNIFORM MESHES FOR SUBDIFFUSION EQUATION