非线性分数阶反应扩散方程组的间断时空有限元方法

doi:10.12286/jssx.2016.2.143

计算数学 ›› 2016, Vol. 38 ›› Issue (2): 143-160.DOI: 10.12286/jssx.2016.2.143

非线性分数阶反应扩散方程组的间断时空有限元方法

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.

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刘金存, 李宏, 刘洋, 何斯日古楞. 非线性分数阶反应扩散方程组的间断时空有限元方法[J]. 计算数学, 2016, 38(2): 143-160.

Liu Jincun, Li Hong, Liu Yang, He Siriguleng. DISCONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR THE SYSTEM OF NONLINEAR FRACTIONAL REACTION-DIFFUSION EQUATIONS[J]. Mathematica Numerica Sinica, 2016, 38(2): 143-160.

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:2015-04-23 Online:2016-04-15 Published:2016-05-13

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.

关键词： 反应扩散方程组, 全离散格式, 存在唯一性, 稳定性, 误差估计

A time-stepping fully discrete scheme for the system of space fractional reaction-diffusion equations is constructed by the space-time finite element method, which is discontinuous in time and continuous in space. Existence and uniqueness for the solution of the fully discrete scheme are analyzed by combining finite element theory and interpolation theory through the Radau integral formula in time discrete intervals. The scheme is proved to be stable unconditionally. The optimal order error estimates in L^∞(L²) norm are presented in detail. Numerical examples are given to illustrate the validity of theoretical analysis.

Key words: system of reaction-diffusion equations, fully discrete scheme, existence and uniqueness, stable unconditionally, error estimate

MR(2010)主题分类:

65M12
65M60

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摘要

非线性分数阶反应扩散方程组的间断时空有限元方法

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

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