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四阶分数阶扩散波动方程的两网格混合元快速算法

王金凤1, 尹保利2, 刘洋2, 李宏2   

  1. 1. 内蒙古财经大学统计与数学学院, 呼和浩特 010070;
    2. 内蒙古大学数学科学学院, 呼和浩特 010021
  • 收稿日期:2021-01-29 出版日期:2022-11-14 发布日期:2022-11-08
  • 通讯作者: 刘洋,Email:mathliuyang@imu.edu.cn.
  • 基金资助:
    国家自然科学基金项目(12061053,12161063),内蒙古自然科学基金项目(2021MS01018,2022LHMS01004),内蒙古自治区高校创新团队项目(NMGIRT2207),“草原英才”工程青年创新创业人才项目资助.

王金凤, 尹保利, 刘洋, 李宏. 四阶分数阶扩散波动方程的两网格混合元快速算法[J]. 计算数学, 2022, 44(4): 496-507.

Wang Jinfeng, Yin Baoli, Liu Yang, Li Hong. A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION[J]. Mathematica Numerica Sinica, 2022, 44(4): 496-507.

A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION

Wang Jinfeng1, Yin Baoli2, Liu Yang2, Li Hong2   

  1. 1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China;
    2. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • Received:2021-01-29 Online:2022-11-14 Published:2022-11-08
本文研究四阶分数阶扩散波动方程模型的基于新混合元方法的快速两网格算法.讨论该方法的稳定性,推导三个未知函数的$L^2$模意义下的最优误差估计.最后通过数值例子验证两网格混合元算法的高效性和理论结果的正确性.
In this paper, a two-grid mixed element algorithm is proposed to solve a fourth-order fractional diffusion-wave model. The stability of the studied two-grid mixed element algorithm is proven, and the optimal a priori error estimates in L2-norm for three unknown functions are derived. Finally, the numerical results are calculated to verify the efficiency of the algorithm and the correctness of the theory results.

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