Speaker: Buyang Li received his Ph.D. degree from City University of Hong Kong in 2012. After that, he worked at Nanjing University (2013-2016), University of Tübingen (2015-2016), and The Hong Kong Polytechnic University (2016-present). Currently, he is Professor at The Hong Kong Polytechnic University. He received the 2022 Hong Kong Mathematical Society Young Scholar Award, and received the 2023 Hong Kong Research Grants Council Research Fellow Award, and the 2023 President’s Award of The Hong Kong Polytechnic University. His research areas mainly focus on scientific computation and numerical analysis of partial differential equations, including numerical methods and analysis of geometric curvature flow and free interface problems, numerical approximation of nonsmooth solutions of nonlinear dispersive equations and wave equations, numerical solutions of incompressible Navier Stokes equations, and so on.

Date: November 8, 2024

Time: 9:00-10:00 am

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

In contrast with the diffusion equation which smoothens the initial data to C_∞ for t>0 (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally cannot expect high-order accuracy in space in solving the subdiffusion equation with nonsmooth initial data. In this paper, a new splitting of the solution is constructed for high-order finite element approximations 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. Extensive numerical experiments are presented to support the theoretical analysis and to illustrate the performance of the proposed high-order splitting finite element methods.

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https://www.view.sdu.edu.cn/info/1020/196532.htm