分数阶对流方程的全离散间断Galerkin方法

李晓婷; 王震

doi:10.21656/1000-0887.450341

分数阶对流方程的全离散间断Galerkin方法

doi: 10.21656/1000-0887.450341

李晓婷¹,
王震^2, ,

1. 江苏大学京江学院，江苏镇江 212013;
2. 江苏大学数学科学学院，江苏镇江 212013

基金项目:

国家自然科学基金（12101266）

详细信息

作者简介:
李晓婷（1987—），女，讲师，硕士(E-mail: lixiaoting@ujs.edu.cn)；王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

通讯作者:
王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

中图分类号: O241.82
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- 文章访问数: 16
- HTML全文浏览量: 1
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-30
- 修回日期: 2025-02-17
- 网络出版日期: 2025-12-31

A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations

LI Xiaoting¹,
WANG Zhen^{2
, ,}

1. Jingjiang College, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R.China;
2. School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R.China

Funds:

The National Science Foundation of China(12101266)

摘要

摘要: 分数阶导数因其在描述自然界中的反常现象方面具有优势而受到广泛关注.研究了一类含时间Caputo-Hadamard分数阶导数的对流方程的数值解法, 采用L1方法近似时间导数, 运用间断Galerkin有限元方法对空间方向进行逼近, 进而得到该方程的全离散数值格式.借助离散的Gronwall不等式分析了格式的稳定性、收敛性及误差估计, 最后通过数值例子验证了理论分析的正确性.
- 分数阶对流 /
- 间断Galerkin方法 /
- 全离散 /
- 稳定性 /
- 收敛性
Abstract: Fractional derivatives have received extensive attention due to their advantages in describing anomalous phenomena in nature. The numerical solutions to a class of convection equations containing temporal Caputo-Hadamard fractional derivatives were studied. The L1 method was adopted to approximate the time derivative, and the discontinuous Galerkin finite element method was used to approximate the spatial direction, thus to obtain the fully discrete numerical scheme for the equations. With the discrete Gronwall inequality, the stability, convergence and error estimates of the scheme were analyzed. Finally, numerical examples verify the correctness of the proposed theoretical method.
- fractional convection /
- discontinuous Galerkin method /
- fully discrete /
- stability /
- convergence

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参考文献(18)

[2]KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and Applications of Fractional Differential Equations[M]. Amsterdam: Elsevier, 2006: 69-132.

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分数阶对流方程的全离散间断Galerkin方法

doi: 10.21656/1000-0887.450341

作者简介:
李晓婷（1987—），女，讲师，硕士(E-mail: lixiaoting@ujs.edu.cn)；王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

通讯作者:
王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

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A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations

计量

目录

留言板

分数阶对流方程的全离散间断Galerkin方法

doi: 10.21656/1000-0887.450341

作者简介: 李晓婷（1987—），女，讲师，硕士(E-mail: lixiaoting@ujs.edu.cn)；王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

通讯作者: 王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

计量

出版历程

A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations

计量

出版历程

目录

作者简介:
李晓婷（1987—），女，讲师，硕士(E-mail: lixiaoting@ujs.edu.cn)；王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).

通讯作者:
王震（1992—），男，副教授，博士，硕士生导师(通讯作者. E-mail: wangzhen@ujs.edu.cn).