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

主講人：李光蓮 香港大學(xué)數(shù)學(xué)系助理教授

時(shí)間：2023年12月7日10：00

地點(diǎn)：騰訊會議 767 652 711

舉辦單位：數(shù)理學(xué)院

主講人介紹：李光蓮，2015年畢業(yè)于美國德州農(nóng)工大學(xué)，獲數(shù)學(xué)博士學(xué)位。2015至2019年作為博士后先后在德國波恩大學(xué)和英國帝國理工大學(xué)工作。2019年至2020年在荷蘭格羅寧根大學(xué)工作，擔(dān)任助理教授。2020年至今在香港大學(xué)數(shù)學(xué)系工作。李光蓮老師的研究方向是多尺度建模的理論和數(shù)值方法，已在SIAM Journal on Numerical Analysis、SIAM Multiscale Modeling and Simulation、Inverse Problems、Journal of Computational Physics等國際一流學(xué)術(shù)期刊上發(fā)表了近三十篇論文，目前是Journal of Computational and Applied Mathematics的副主編。

內(nèi)容介紹：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).