汇报标题 (Title)：High-order splitting finite element methods for the subdiffusion equation with limited smoothing property (拥有有限光滑性的亚扩散方程高阶割裂有限元步骤)
汇报人 (Speaker)：周知 副教授（香港理工大学）
汇报功夫 (Time)：2023年11月8日(周三) 14:00
汇报地址 (Place)：腾讯会议(537 367 798)
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：In contrast with the diffusion equation which has an inifinitely smoothing property, the subdiffusion equation only exhibits limited spatial regularity. As a result, one cannot expect high-order accuracy in space when solving the subdiffusion equation with nonsmooth initial data. In this talk, I will introduce a new high-order finite element approximation to the subdiffusion equation with nonsmooth initial data. The method is constructed by splitting the solution into two parts, i.e., a time-dependent smooth part and a time-independent nonsmooth part, and then approximating the two parts via different strategies. The time-dependent smooth part is approximated by using high-order finite element method in space and convolution quadrature in time, while the steady nonsmooth part could be approximated by using smaller mesh size or other methods that could yield high-order accuracy. Several examples are presented to show how to accurately approximate the steady nonsmooth part, including piecewise smooth initial data, Dirac–Delta point initial data, and Dirac measure concentrated on an interface. The argument could be directly extended to subdiffusion equations with nonsmooth source data.
