四阶分数阶扩散波动方程的两网格混合元快速算法  

A FAST TWO-GRIDMIXED ELEMENT METHODFOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION

作　　者：王金凤 尹保利 刘洋[2] 李宏 Wang Jinfeng;Yin Baoli;Liu Yang;Li Hong(School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China;School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[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

出　　处：《计算数学》2022年第4期496-507,共12页Mathematica Numerica Sinica

基　　金：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.

摘　　要：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 L^(2)-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.

关 键 词：四阶时间分数阶扩散波动方程 修正L1公式 两网格算法 混合元方法 误差估计 

分 类 号：O241.8[理学—计算数学]