报告问题 (Title)：High-order splitting finite element methods for the subdiffusion equation with limited smoothing property (具有有限平滑性的亚扩散方程高阶破碎有限元要领)

报告人 (Speaker)：周知 副教授（香港理工大学）

报告时间 (Time)：2023年11月8日(周三) 14:00

报告所在 (Place)：腾讯聚会(537 367 798)

约请人(Inviter)：李常品、蔡敏

主理部分：理学院数学系

报告摘要：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.