10月15日 许悦瑾博士学术报告

发布时间:2025-10-14

报告题目：Efficient numerical methods for solving parabolic equations

主讲人：许悦瑾博士，澳门大学 

报告时间：2025年10月15日（周三），9:00-10:00

报告地点：计算机学院A501

主持人：江颖教授

摘要：

In our recent work, we mainly proposed some efficient numerical methods for solving parabolic equations. For equations in regular domains, we proposed the EIFE method by using the finite element method for spatial discretization and exponential Runge-Kutta approach for temporal discretization. Under certain regularity assumptions, error estimates measured in H¹-norm are derived for the proposed schemes with one and two RK stages. For equations in general irregular domains, we used the diffuse domain method to extend the original parabolic problem to a similar but slightly modified problem defined over a larger regular domain. Based on the weighted Sobolev spaces, we rigorously established the convergence of the diffuse domain solution to the original solution as the interface thickness parameter goes to zero, together with the corresponding optimal error estimates under the weighted  L² and  H¹ norms.

主讲人简介：

Dr. Xu obtained her bachelor degree in 2019 from Sun Yat-sen University, and then studied at the Shanghai Jiao Tong University and earned her PhD degree in 2024. Later, she worked as a postdoctoral scholar at Penn State University for one year. Now, she is a postdoctoral fellow at the University of Macau. Her research mainly concentrated on designing the fast and efficient algorithm for solving parabolic equations and deriving the corresponding error estimate. Her work has appeared in some premier journals, such as SIAM Journal on Scientific Computing, Numerical Methods for Partial Differential Equations.