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

页码：587 / 606

页数：20

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