时空分数阶对流-弥散方程组的有限元方法

doi:10.3969/j.cnki.jdxb.2016.01.002

journal6 ›› 2016, Vol. 37 ›› Issue (1): 7-10.DOI: 10.3969/j.cnki.jdxb.2016.01.002

时空分数阶对流-弥散方程组的有限元方法

吴红英

（怀化学院数学与计算科学学院，湖南怀化 418008)

出版日期:2016-01-25 发布日期:2016-01-21
作者简介:吴红英（1974—)，女，湖南张家界人，怀化学院数学与计算科学学院副教授，硕士，主要从事数值计算研究.

Finite Element Solution to Advection-Dispersion Equations with Time-Space Fractional Derivatives

WU Hong-Ying

(School of Mathematics Computation Science，Huaihua University，Huaihua 418008，Hunan China)

Online:2016-01-25 Published:2016-01-21

摘要/Abstract

摘要：时间空间分数阶对流-弥散方程组一般没有解析解，有限元方法是进行数值模拟的有效途径.先对微分方程组进行时间半离散，然后推导出固定时间层的变分公式和有限元方程组，同时给出求解有限元解的一种线性迭代算法.数值实例表明，三次有限元迭代算法的时空收敛阶分别为 2－α_i和4.

关键词： 分数阶对流-弥散方程组, 分数微分算子, 变分问题, 有限元方法, 迭代算法

Abstract: Generally，there is no analytical solution for time-space fractional advection-dispersion equations.The finite element method is the effective approach for numerical simulation.In this article a time-semi discrete variable formulas and the corresponding FE equations are derived.Numerical example illustrates that the FEM iteration algorithm has 2－α_i order and fourth order convergence rates for time and space，respectively.

Key words: fractional advection-dispersion equations, fractional differential operations, variable formulas, iteration algorithm

吴红英. 时空分数阶对流-弥散方程组的有限元方法[J]. journal6, 2016, 37(1): 7-10.

WU Hong-Ying. Finite Element Solution to Advection-Dispersion Equations with Time-Space Fractional Derivatives[J]. journal6, 2016, 37(1): 7-10.

参考文献

[1] BORIS BAEUMER，MIHLY KOVCS，MARK M MEERSCHAERT.Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels[J].Bulletin Mathematical Biology，2007，69(7):2 281-2 297.

[2] BORIS BAEUMER，MIHLY KOVCS，MARK M MEERSCHAERT.Numerical Solutions for Fractional Reaction-Diffusion Equation[J].Computers & Mathematics with Applications,2008,55:2 212-2 226.

[3] HERMANN BRUNNERA，LEEVAN LINGA，MASAHIRO YAMAMOTO.Numerical Simulations of 2D Fractional Subdiffusion Problems[J].Journal Computational Physics，2010，229(18):6 613-6 622.

[4] ALBERTO CABADA，ZAKARIA HAMDI.Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions[J].Applied Mathematics and Computation，2014，228:251-257.

[5] ALI YAKAR，MEHMET EMIR KOKSAL，ALLABEREN ASHYRALYEV.Existence Results for Solutions of Nonlinear Fractional Differential Equations[J/OL].Abstract and Applied Analysis，2012:Article ID 267108[2015-01-20].http:∥www.hindawi.com/journals/aaa/2012/267108/.

[6] G J FIX，J P ROOP.Least Squares Finite-Element Solution of a Fractional Order Two-Point Boundary Value Problem[J].Computers & Mathematics with Applications，2004，48(7):1 017-1 033.

[7] JIANG Yingjun，MA Jingtang.Moving Finite Element Methods for Time Fractional Partial Differential Equations[J].Science China Mathematics，2013，56(6):1 287-1 300.

[8] VINCENT J ERVIN，JOHN PAUL ROOP.Variational Formulation for the Stationary Fractional Advection Dispersion Equation[J].Numer. Methods Partial Differential Equations，2006,22:558-576.

[9] VINCENT ERVIN，JOHN PAUL ROOP.Variational Solution of Fractional Advection Dispersion Equations on Bounded Domains in Rd[J].Numer. Methods Partial Differential Equations，2007，23:256-281.

[10] VINCENT ERVIN，NORBERT HEUER，JOHN PAUL ROOP.Numerical Approximation of a Time Dependent，Nonlinear，Space-Fractional Diffusion Equation[J].SIAM Journal Numerical Analysis，2007，45(2):572-591.

[11] ZHOU Z Q，WU H Y.Finite Element Multigrid Method for the Boundary Value Problem of Fractional Advection Dispersion Equation[J/OL].Journal of Applied Mathematics，2013:Article ID 385463[2015-02-12].http:∥dx.doi.org/10.1155/2013/385463.

时空分数阶对流-弥散方程组的有限元方法

Finite Element Solution to Advection-Dispersion Equations with Time-Space Fractional Derivatives

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

编辑推荐

Metrics

本文评价

[1]	胡志增，梁开福. 基于共轭梯度迭代算法受控AR模型的参数辨识[J]. 吉首大学学报（自然科学版）, 2016, 37(6): 29-33.
[2]	刘传清. 认知无线电协作频谱感知混合加权算法[J]. journal6, 2010, 31(5): 50-54.
[3]	李红刚. 非线性混合变分包含的Ishikawa迭代过程与稳定性[J]. journal6, 2008, 29(5): 14-18.
[4]	游华. 加权最小二乘估计中选择权数的迭代算法[J]. journal6, 2007, 28(4): 27-29.
[5]	姜子文, 姜艳. 均匀棒纯纵向运动初值问题的混合有限元方法[J]. journal6, 2007, 28(1): 7-13.