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非线性分数阶反应扩散方程组的间断时空有限元方法

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刘金存, 李宏, 刘洋, 何斯日古楞
内蒙古大学数学科学学院, 呼和浩特 010021
收稿日期:2015-04-23出版日期:2016-04-15发布日期:2016-05-13


基金资助:国家自然科学基金(11361035,11301258)和内蒙古自然科学基金(2012MS0106,2012MS0108,2014BS0101)资助项目.


DISCONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR THE SYSTEM OF NONLINEAR FRACTIONAL REACTION-DIFFUSION EQUATIONS

Liu Jincun, Li Hong, Liu Yang, He Siriguleng
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Received:2015-04-23Online:2016-04-15Published:2016-05-13







摘要



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利用时间间断空间连续的时空有限元方法构造了空间分数阶反应扩散方程组的可以逐时间层求解的全离散格式.在时间离散区间上,采用Radau积分公式,将插值理论与有限元理论相结合,给出了全离散格式解的存在唯一性结果,并证明了所给格式是无条件稳定的,进而详细给出最优阶L(L2)模误差估计过程.最后用数值算例验证了理论分析的正确性.
MR(2010)主题分类:
65M12
65M60

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[1] Podlubny I. Fractional Differential Equations[M]. New York:Academic Press, 1999.

[2] Liu F, Zhuang P, Anh V, Turner I, Burrage K. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation[J]. Appl. Math. Comput., 2007, 191:12-20.

[3] Sun Z Z, Wu X N. A fully discrete difference scheme for a diffusion-wave system[J]. Appl. Numer. Math., 2006, 56:193-209.

[4] Yuste S B, Acedo L. An explicit finite difference method and a new von Numann-type stability analysis for fractional diffusion equation[J]. SIAM J. Numer. Anal., 2005, 42:1862-1874.

[5] Li X J, Xu C J. Existence and uniqueness of the weak solution of the space-time fractional diffusion equation and a spectral method approximation[J]. Commun. Comput. Phys., 2010, 8(5):1016-1051.

[6] Ervin V J, Roop J P. Variational formaulation for the stationary fractional advection dispersion equation[J]. Numer. Methods Partial Differential Equations, 2006, 22(3):558-576.

[7] Deng W H. Finite element method for the space and time fractional Fokker-Planck equation[J]. SIAM J. Numer. Anal., 2008, 47:204-226.

[8] Zhang H, Liu F, Anh V. Galerkin finite element approximation of symmetric space-fractional partial differential equations[J]. Appl. Math. Comput., 2010, 217:2534-2545.

[9] Li C P, Zhao Z G, Chen Y Q. Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion[J]. Comput. Math. Appl., 2011, 62:855-875.

[10] Ford N J, Xiao J Y, Yan Y B. A finite element method for time fractional partial differential equations[J]. Fract. Calc. Appl. Anal., 2011, 14:454-574.

[11] Bu W P, Liu X T, Tang Y F, Yang J Y. Finite element multigrid method for multi-term time fractional advection diffusion equations[J]. Int. J. Model. Simul. Sci. Comput., 2015, 6 DOI:10.1142/S1793962315400012.

[12] Mustapha K, McLean W. Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation[J]. Numer. Algor., 2011, 56:159-184.

[13] Zheng Y Y, Li C P, Zhao Z G. A fully discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation[J]. Math. Probl. Eng., 2010, Article ID 279038, 26 pages.

[14] 刘金存, 李宏. A space-time finite element method for the semilinear fractional diffusion equation:the discontinuous Galerkin method[J]. 应用数学, 2013, 26(4):853-862.

[15] Ahmad B, Alhothuali M S, Alsulami H H, Kirane M, Timoshin S. On nonlinear nonlocal systems of reaction diffusion equations[J]. Abstr. Appl. Anal., 2014, Article ID 804784, 6 pages.

[16] Karakashian C, Makridakis C. A space-time finite element method for the nonlinear Schrödinger the discontinuous Galerkin method[J]. Math. Comp., 1998, 97(222):479-499.

[17] Yang Q, Liu F, Turner I. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Model., 2010, 34:200-218.

[18] Davis P J, Rabinowitz P. Methods of Numerical Integration[M]. New York:Academic Press, 1975.

[19] Brenner B C, Scott L R. The Mathematical Theory of Finite Element Methods[M]. New York:Springer-verlag, 1994.

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