报告题目 (Title)：Local error estimates of some numerical schemes for a multi-term time-fractional diffusion equation (多项时间分数阶扩散方程的一些数值格式的局部误差估计)

报告人 (Speaker)： 陈虎 副教授（中国海洋大学）

报告时间 (Time)：2022年10月13日(周四) 10:15-11:45

报告地点 (Place)：线上腾讯会议 （会议 ID：650 523 449）

邀请人(Inviter)：李常品、蔡敏

主办部门：理学院数学系

报告摘要：In this talk, we consider the time-fractional initial-boundary problems of parabolic type. Previously, global error bounds for computed numerical solutions to such problems have been provided by Liao et al. (SIAM J. Numer. Anal. 2018, 2019) and Stynes et al. (SIAM J. Numer. Anal. 2017). In this talk we show how the concept of complete monotonicity can be combined with these older analyses to derive local error bounds (i.e., error bounds that are sharper than global bounds when one is not close to the initial time t = 0). Furthermore, we show that the error analyses of the above papers are essentially the same – their key stability parameters, which seem superficially different from each other, become identical after a simple rescaling. Our new approach is used to bound the global and local errors in the numerical solution of a multi-term time-fractional diffusion equation, using the L1 scheme for the temporal discretisation of each fractional derivative. These error bounds are $\alpha$-robust. Numerical results show they are sharp.