• 论文 •

### 分数阶对流-弥散方程的移动网格有限元方法

1. 怀化学院数学系, 湖南怀化 418008
• 收稿日期:2012-04-16 出版日期:2014-03-15 发布日期:2014-03-14
• 基金资助:

湖南省教育厅科研基金（07C505）资助项目

Zhou Zhiqiang, Wu Hongying. MOVING MESH FINITE ELEMENT METHOD FOR FRACTIONAL ADVECTION DISPERSION EQUATION[J]. Journal of Numerical Methods and Computer Applications, 2014, 35(1): 1-7.

### MOVING MESH FINITE ELEMENT METHOD FOR FRACTIONAL ADVECTION DISPERSION EQUATION

Zhou Zhiqiang, Wu Hongying

1. Department of Mathematics, Huaihua University, Huaihua 418008, Hunan, China
• Received:2012-04-16 Online:2014-03-15 Published:2014-03-14

Compared with classical advection dispersion equation, fractional advection dispersion equation(FADE) includes non-local differential operators, which leads to calculating numerical integrals with weakly singular kernel on every elements. As the fractional order μ in the dispersion term tends to 1, penetration curves evolve to be heavy-tailed plumes and oscillations are visible in computed solutions. Studies show that the stiffness matrix of time semi-discretization can be calculated directly by formulas established from a special variational formulation. Numerical oscillations are eliminated by using adaptive moving mesh and De Boor algorithm, while the number of nodes remains unchanged.

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 [1] Benson D A, Wheatcraft S W and Meerschaeert M M. The fractional order govering equations of Lévy motion, Water Ressour Res[J]. 2000, 36(6): 1403-1412.[2] Benson D A, Wheatcraft S W and Meerschaeert M M. Application of fractional advectiondispersion equation[J]. Water Ressour Res, 2000, 36(6): 1413-1423.[3] Benson D A, Wheatcraft S W and Meerschaeert M M. fractional dispersion, Lévy motion, and the MADE tracer test[J]. Transport in Porous Media, 2001, 42: 211-240.[4] Podlubny I. Fractional Differential Equations. New York, Academic press, 1999.[5] Ervin V J and Roop J P. variational formulation for the stational fractional advection dispersion equation[J]. Numer. meth. P.D.E., 2006, 22(3): 558-576.[6] Deng W H. Finite element method for the space and time fractional Fokker-Planck equation[J]. SIAM J. Numer. Anal., 2008, 47: 204-206.[7] Li X J, Xu C J. existence and uniqueness of the weak solution of the space-time fractional diffusion and a spectral method approximation[J]. Commun. Comput. Phys., 2010, 8(5): 1016-1051.[8] Huang W and Russell R D. Adaptive Moving Mesh Methods. British Columbia, Springer press, 2010.[9] Ma J T and Jiang Y J. Moving collocation methods for time fractional differential equations and simulation of blowup[J]. Sci. China Math., 2011, 54(3): 611-622.
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