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时间分数阶扩散方程的一类三次有限体积元方法
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Abstract:
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.
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