Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2020-06-03 , DOI: 10.1007/s10915-020-01238-5 Jiliang Cao , Aiguo Xiao , Weiping Bu
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.
中文翻译:
回火时间分数阶对流-弥散方程的有限差分/有限元方法,可快速估算Caputo导数
本文考虑了一类具有Caputo回火分数导数的分数阶对流扩散方程。提出了一种评估卡普托回火分数微分的有效算法,可大大减少计算工作量和存储量,这对大规模问题具有重要意义。基于非光滑正则性假设,通过有限差分法及时得到半离散形式,并研究其稳定性和收敛性。然后通过有限元方法,导出相应的完全离散方案并讨论其收敛性。最后,给出了基于不同领域的数值算例,以证明数值方案的有效性并验证了理论分析。