Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	陈虎博士，中国海洋大学数学科学学院
Inviter:	唐贻发研究员
Title:	Using complete monotonicity to deduce local error estimates for discretisations of a multi-term time-fractional diffusion equation
Time & Venue:	2022.05.17 14:00-15:00 腾讯会议ID：141-927-701
Abstract:	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.