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

Quan, Chaoyu1,2; Wu, Xu3,4

2023

10.1137/22M1506468

SIAM JOURNAL ON NUMERICAL ANALYSIS   影响因子和分区

0036-1429

1095-7170

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.

L2-type method subdiffusion equation graded mesh positive semidefiniteness H1-norm stability and convergence

SCI ; EI

英语

通讯

National Natural Sci-ence Foundation of China[12271241] ; Guangdong Basic and Applied Basic Research Foundation[2023B1515020030] ; Shenzhen Science and Technology Program[RCYX20210609104358076]

Mathematics

Mathematics, Applied

WOS:001082987300005

SIAM PUBLICATIONS

20234414982342

Convergence of numerical methods ; Grading ; Partial differential equations

Calculus:921.2 ; Numerical Methods:921.6

MATHEMATICS

Web of Science

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

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):2106-2132.

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),2106-2132.

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):2106-2132.