L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

doi:10.1007/s42967-023-00257-x

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (1): 203-227.doi: 10.1007/s42967-023-00257-x

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L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

Zhen Wang

School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China

收稿日期:2023-01-09 修回日期:2023-01-14 接受日期:2023-02-01 出版日期:2025-04-21 发布日期:2025-04-21
通讯作者: Zhen Wang,wangzhen@ujs.edu.cn E-mail:wangzhen@ujs.edu.cn
基金资助:
ZW was partially supported by the National Natural Science Foundation of China under Grant No. 12101266.

L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

Zhen Wang

School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China

Received:2023-01-09 Revised:2023-01-14 Accepted:2023-02-01 Online:2025-04-21 Published:2025-04-21
Supported by:
ZW was partially supported by the National Natural Science Foundation of China under Grant No. 12101266.

摘要/Abstract

摘要： In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be α-robust using the newly established Gronwall inequalities, that is, it remains valid when α → 1^-. Numerical experiments are given to demonstrate the theoretical statements.

关键词: Caputo-Hadamard derivative, Discrete Gronwall inequality, L1 formula, Local discontinuous Galerkin (LDG) method, Error estimate

Abstract: In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be α-robust using the newly established Gronwall inequalities, that is, it remains valid when α → 1^-. Numerical experiments are given to demonstrate the theoretical statements.

Key words: Caputo-Hadamard derivative, Discrete Gronwall inequality, L1 formula, Local discontinuous Galerkin (LDG) method, Error estimate

中图分类号:

Zhen Wang. L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation[J]. Communications on Applied Mathematics and Computation, 2025, 7(1): 203-227.

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L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

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