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分数阶对流-弥散方程的移动网格有限元方法

周志强, 吴红英   

  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

周志强, 吴红英. 分数阶对流-弥散方程的移动网格有限元方法[J]. 数值计算与计算机应用, 2014, 35(1): 1-7.

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
相比经典的对流-弥散方程,分数微分算子的非局部性质导致分数阶对流-弥散方程 (FADE)的有限元方法在每个单元上的计算都联系一个带弱奇异核的数值积分.当弥散项分数阶μ 接近1 时,穿透曲线出现重度拖尾,数值解产生振荡. 研究表明:时间半离散后的FADE 在特殊的变分形式下,有限元刚度矩阵有直接计算公式;以De Boor算法为基础的移动网格方法能很好地消除数值振荡.
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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