Wavelet-based Edge MsFEM for Singularly Perturbed Convection-Diffusion Equations

主讲人：李光莲 香港大学数学系助理教授

时间：2023年12月7日10：00

地点：腾讯会议 767 652 711

举办单位：数理学院

主讲人介绍：李光莲，2015年毕业于美国德州农工大学，获数学博士学位。2015至2019年作为博士后先后在德国波恩大学和英国帝国理工大学工作。2019年至2020年在荷兰格罗宁根大学工作，担任助理教授。2020年至今在香港大学数学系工作。李光莲老师的研究方向是多尺度建模的理论和数值方法，已在SIAM Journal on Numerical Analysis、SIAM Multiscale Modeling and Simulation、Inverse Problems、Journal of Computational Physics等国际一流学术期刊上发表了近三十篇论文，目前是Journal of Computational and Applied Mathematics的副主编。

内容介绍：We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) to solve the singularly perturbed convection diffusion equations. The main idea is to first establish a local splitting of the solution over a local region by a local bubble part and local Harmonic extension part, and then derive a global splitting by means of Partition of Unity. This facilitates a representation of the solution as a summation of a global bubble part and a global Harmonic extension part, where the first part can be computed locally in parallel. To approximate the second part, we construct an edge multiscale ansatz space locally with hierarchical bases as the local boundary data that has a guaranteed approximation rate without higher regularity requirement on the solution. The key innovation of this proposed WEMsFEM lies in a provable convergence rate with little restriction on the mesh size or the regularity of the solution. Its convergence rate with respect to the computational degree of freedom is rigorously analyzed, which is verified by extensive 2-d and 3-d numerical tests. This is a joint work with Eric Chung (The Chinese University of Hong Kong, China) and Shubin Fu (Eastern Institute of Technology, China).