Finite element method for two-dimensional space-fractional advection-dispersion equations

被引：68

作者：

Zhao, Yanmin ^{[1
]}

Bu, Weiping ^{[2
]}

Huang, Jianfei ^{[3
]}

Liu, Da-Yan ^{[4
]}

Tang, Yifa ^{[2
]}

机构：

[1] Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China

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

[3] Qingdao Univ, Coll Math, Qingdao 266071, Peoples R China

[4] Univ Orleans, INSA, Ctr Val Loire, PRISME EA 4229, Bourges, France

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 257卷

基金：

中国国家自然科学基金;

关键词：

Space-fractional advection-dispersion equation; Backward Euler scheme; Crank-Nicolson-Galerkin scheme; Finite element method; Optimal error estimate; DIFFERENCE APPROXIMATIONS; ADOMIAN DECOMPOSITION; NUMERICAL-METHOD; SPECTRAL METHOD; DIFFUSION;

D O I：

10.1016/j.amc.2015.01.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The backward Euler and Crank-Nicolson-Galerkin fully-discrete approximate schemes for two-dimensional space-fractional advection-dispersion equations are established. Firstly, we prove that the corresponding variational problem has a unique solution, and the proposed fully-discrete schemes are unconditionally stable, whose solutions are all unique. Secondly, the optimal error estimates are derived by use of properties of projection operator and fractional derivatives. Finally, numerical examples demonstrate effectiveness of numerical schemes and confirm the theoretical analysis. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：553 / 565

页数：13

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