Finite Difference/Finite Element Method for Tempered Time Fractional Advection-Dispersion Equation with Fast Evaluation of Caputo Derivative
Finite Difference/Finite Element Method for Tempered Time Fractional Advection-Dispersion Equation with Fast Evaluation of Caputo Derivative
复制标题
具有快速求导卡普托导数的修正时间分数阶平流色散方程的有限差分/有限元法
DOI：
10.1007/s10915-020-01238-5
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发表时间：
2020
影响因子：
2.5
通讯作者：
Bu Weiping
中科院分区：
文献类型：
--
作者：
Cao Jiliang;Xiao Aiguo;Bu Weiping
本文用数值方法研究了一类具有Caputo调质分数阶导数的分数阶平流色散方程。提出了一种高效的Caputo回火分数阶导数求值算法，大大减少了计算量和存储空间，对求解大规模问题具有重要意义。基于非光滑正则性假设，用有限差分法在时间上得到了半离散形式，并研究了其稳定性和收敛性。然后用有限元法推导了相应的全离散格式，并讨论了其收敛性。最后给出了基于不同领域的数值算例，验证了数值格式的有效性和理论分析的正确性。
In this paper, a class of fractional advection–dispersion equations with Caputo tempered fractional derivative are considered numerically. An efficient algorithm for the evaluation of Caputo tempered fractional derivative is proposed to sharply reduce the computational work and storage, and this is of great significance for large-scale problems. Based on the nonsmooth regularity assumptions, a semi-discrete form is obtained by finite difference method in time, and its stability and convergence are investigated. Then by finite element method, we derive the corresponding fully discrete scheme and discuss its convergence. At last, some numerical examples, based on different domains, are presented to demonstrate effectiveness of numerical schemes and confirm the theoretical analysis.