时间分数阶扩散方程的一类三次有限体积元方法  

A Cubic Finite Volume Element Method for the Time Fractional Diffusion Equation

作　　者：何斯日古楞 澈力木格 高晶英 

机构地区：[1]呼和浩特民族学院,数学与大数据学院,内蒙古 呼和浩特 [2]呼和浩特民族学院,计算机科学与信息工程学院,内蒙古 呼和浩特

出　　处：《应用数学进展》2022年第8期5529-5535,共7页Advances in Applied Mathematics

摘　　要：本文基于应力佳点对偶网格剖分以及分片三次Lagrange插值试探函数空间和分片常数检验函数空间的三次有限体积元法和Caputo导数的L1-逼近公式构造数值格式求解一维时间分数阶扩散方程,并证明了格式的L2范数在时间和空间方向分别 阶和四阶收敛误差估计。通过数值实验验证了理论分析结果以及所提格式的有效性。In this article, the one-dimensional time fractional diffusion equation is solved by a numerical scheme which is constructed by the L1-formula of approximating the Caputo fractional derivative and a cubic finite volume element method. The cubic finite volume element method is based on the optimal stress points dual partition, and the trial function space of piecewise cubic Lagrange inter-polation and the test function space of piecewise constant. The L2-norm error estimate of fourth or-der convergence in space and order convergence in time is proved. Numerical experiments are given to verify the effectiveness of the theoretical analysis results and the proposed scheme.

关 键 词：时间分数阶扩散方程 三次有限体积元法 L1-公式 

分 类 号：O175[理学—数学]