Speaker: Prof. Jie Shen (沈捷教授)

Time: 13:30-14:30, 25 February 2022 (Friday) (Beijing time)

Venue: 华信书院, CC126

Abstract

Solutions for a large class of partial differential equations (PDEs) arising from sciences and engineering applications are required to be positive to be positive or within a specified bound.

It is of critical importance that their numerical approximations preserve the positivity/bound at the discrete level, as violation of the positivity/bound preserving may render the discrete problems ill posed. I will review the existing approaches for constructing positivity/bound preserving schemes, and then present several efficient and accurate approaches which are relative easy to implement and can be combined with most spatial discretization.

About Prof. Shen

Professor Shen's research interests are numerical analysis and scientific computing with applications in computational fluid dynamics and materials science. He has made major contributions in many areas of numerical analysis and scientific computation, including the design and analysis of efficient numerical schemes for Navier-Stokes equations and the development of spectral-Galerkin methods for a broad class of partial differential equations. He serves on the editorial boards of several leading international research journals and has authored or co-authored over 100 peer-reviewed research articles. He was awarded a Fulbright "Research Chair" in 2008 and a "Chang Jiang Chair Professorship" by the Ministry of Education of China in 2010. He was named as one of the members of the 2017 Class of American Mathematical Society (AMS) and one of the members of the 2020 Class of Society for Industrial and Applied Mathematics.