Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation

被引：74

作者：

Li, Limei ^{[1
]}

Xu, Da ^{[2
]}

Luo, Man ^{[2
]}

机构：

[1] Hunan Inst Sci & Technol, Dept Math, Yueyang 414000, Peoples R China

[2] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2013年 / 255卷

基金：

中国国家自然科学基金;

关键词：

Fractional diffusion-wave equation; Alternating direction implicit method; Galerkin finite element method; Crank-Nicolson method; ANOMALOUS DIFFUSION; DIFFERENCE/SPECTRAL APPROXIMATIONS; SPECTRAL METHOD; RANDOM-WALK; SPACE; SCHEME; STABILITY;

D O I：

10.1016/j.jcp.2013.08.031

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

New numerical techniques are presented for the solution of the two-dimensional fractional diffusion-wave equation with a time fractional derivative of order alpha (1 < alpha < 2). In these methods, Galerkin finite element is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) method based on the Crank-Nicolson method are considered. The unconditional stability and L-2 norm convergence of the ADI scheme are proved rigorously. Numerical results are presented to support our theoretical analysis. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：471 / 485

页数：15

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