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 , where and is convex or smooth. The differential equation is , where each is a Caputo derivative with and the 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 “-robust”) if , unlike the bounds in Huang and Stynes (2020), which blow up as . Thus these new error bounds are a more natural and desirable result, since the unknown solution is well behaved as .
中文翻译:
一个 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 ,在哪里 和 是凸的或光滑的。微分方程是,每个 是具有的Caputo衍生物 和 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,“-robust”),如果 与Huang和Stynes(2020)的界限不同 。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:。