Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation

被引：27

作者：

Ren, Jincheng ^{[1
]}

Long, Xiaonian ^{[2
,3
,4
]}

Mao, Shipeng ^{[2
,3
,4
]}

Zhang, Jiwei ^{[5
]}

机构：

[1] Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450045, Henan, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China

[5] Beijing Computat Sci Res Ctr, Beijing 100094, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 72卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Fractional diffusion-wave equation; Finite element method; Fully discrete scheme; Error estimate; NUMERICAL APPROXIMATION; SPACE; SUBDIFFUSION;

D O I：

10.1007/s10915-017-0385-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the error estimates of fully discrete finite element approximation for the time fractional diffusion-wave equation are discussed. Based on the standard Galerkin finite element method approach for the spatial discretization and the L1 formula for the approximation of the time fractional derivative, the fully discrete scheme for solving the constant coefficient fractional diffusion-wave equation is obtained and the superconvergence estimate is proposed and analyzed. Further, a fully discrete finite element scheme is presented for solving the variable coefficient fractional diffusion-wave equation and the corresponding error estimates are also established. Finally, numerical experiments are included to support the theoretical results.

引用

页码：917 / 935

页数：19

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