$$H^{1}$$-norm error analysis of a robust ADI method on graded mesh for three-dimensional subdiffusion problems
$$H^{1}$$-norm error analysis of a robust ADI method on graded mesh for three-dimensional subdiffusion problems
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DOI：
10.1007/s11075-023-01676-w
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发表时间：
2023-10
影响因子：
2.1
通讯作者：
Ziyi Zhou;Haixiang Zhang;Xuehua Yang
中科院分区：
文献类型：
--
作者：
Ziyi Zhou;Haixiang Zhang;Xuehua Yang
本文提出了一种用于求解三维亚扩散问题的梯度网格鲁棒ADI方案。采用L1格式对Caputo分数阶导数进行离散化，采用分级网格消除精确解在初始时刻的弱奇异性。空间导数用有限差分法逼近。基于改进的离散分数阶不等式，证明了该不等式的稳定性和鲁棒范数收敛性，当分数阶导数阶数增加时，误差界不会增大。通过三维数值算例验证了ADI方法的有效性和准确性。同时给出了CPU时间，表明该方法对三维亚扩散问题是非常有效的。
This work proposes a robust ADI scheme on graded mesh for solving three-dimensional subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where the graded mesh is used to eliminate the weak singular behavior of the exact solution at the initial time. The spatial derivatives are approximated by the finite difference method. Based on the improved discrete fractionalinequality, we prove the stability and-robust-norm convergence, in which the error bound does not blow up when the order of fractional derivative. The 3D numerical examples are proposed to verify the efficiency and accuracy of the ADI method. The CPU time is also provided, which shows the proposed method is very efficient for 3D subdiffusion problems.