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An α-robust finite element method for a multi-term time-fractional diffusion problem
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.cam.2020.113334
Chaobao Huang , Martin Stynes , Hu Chen

A time-fractional initial–boundary problem is considered on a bounded spatial domain ΩRd, where d{1,2,3} and Ω is convex or smooth. The differential equation is i=1lqiDtαiu(x,t)Δu(x,t)=f, where each Dtαi is a Caputo derivative with 0<αl<<α1<1 and the qi are positive constants. A new error analysis is given for the numerical method (L1 scheme in time, finite elements in space) of Huang and Stynes (2020). The error bounds that are derived here remain valid (i.e., are “α-robust”) if α11, unlike the bounds in Huang and Stynes (2020), which blow up as α11. Thus these new error bounds are a more natural and desirable result, since the unknown solution is well behaved as α11.



中文翻译:

一个 α项的时间分数阶扩散问题的鲁棒有限元方法

在有界空间域上考虑时间分数初始边界问题 Ω[Rd,在哪里 d{1个23}Ω是凸的或光滑的。微分方程是一世=1个q一世dŤα一世üXŤ-ΔüXŤ=F,每个 dŤα一世 是具有的Caputo衍生物 0<α<<α1个<1个q一世是正常数。对Huang和Stynes(2020)的数值方法(时间上的L1方案,空间中的有限元)进行了新的误差分析。此处得出的误差范围仍然有效(即,“α-robust”),如果 α1个1个-与Huang和Stynes(2020)的界限不同 α1个1个-。因此,这些新的误差范围是更自然且更理想的结果,因为未知解的行为如下:α1个1个-

更新日期:2021-01-07
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