The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Mathematical analysis

被引：25
|
作者：
Li, Changpin [1 ]
Wang, Zhen [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2020年 / 150卷
基金：
中国国家自然科学基金;
关键词：
Caputo derivative; Fractional differential equations; Regularity; Local discontinuous Galerkin method; Convergence;
D O I：
10.1016/j.apnum.2019.11.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In Li and Wang (2019) [11], three kinds of typical Caputo-type partial differential equations are numerically studied via the local discontinuous Galerkin (LDG) finite element methods, including Caputo-type reaction-diffusion equation, Caputo-type reaction-diffusion-wave equation, and Caputo-type cable equation without regularity analysis. In this article, we study the existence, uniqueness, and regularity of the solutions to these equations. Besides, the error estimate for Caputo-type cable equation has been greatly improved. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：587 / 606
页数：20
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