%0 Journal Article
%T 时间分数阶扩散方程的一类三次有限体积元方法<br>A Cubic Finite Volume Element Method for the Time Fractional Diffusion Equation
%A 何斯日古楞
%A 澈力木格
%A 高晶英
%J Advances in Applied Mathematics
%P 5529-5535
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.118582
%X 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。<br />
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.
%K 时间分数阶扩散方程，三次有限体积元法，L1-公式<br>Time Fractional Diffusion Equation
%K Cubic Finite Volume Element Method
%K L1-Formula
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=54664