报告题目：Quasi-Monte Carlo finite element approximation of the Navier--Stokes equations with initial data modeled by log-normal random fields

报告人：李光莲助理教授 香港大学数学系

时间：2023.5.23 上午10:00-11:00

腾讯会议号：131-898-806 （https://meeting.tencent.com/dm/JLncAmbKycZF）

报告摘要：In this talk, we analyze the numerical approximation of the Navier--Stokes problem over a bounded polygonal domain in $\R^2$, where the initial condition is modeled by a log-normal random field. This problem usually arises in the area of uncertainty quantification. We aim to compute the expectation value of linear functionals of the solution to the Navier--Stokes equations and perform a rigorous error analysis for the problem. In particular, our method includes the finite element, fully-discrete discretizations, truncated Karhunen--Lo\'eve expansion for the realizations of the initial condition, and lattice-based quasi-Monte Carlo (QMC) method to estimate the expected values over the parameter space. Our QMC analysis is based on randomly-shifted lattice rules for the integration over the domain in high-dimensional space, which guarantees the error decays with $\mathcal{O}(N^{-1+\delta})$, where $N$ is the number of sampling points, $\delta>0$ is an arbitrary small number, and the constant in the decay estimate is independent of the dimension of integration. This is a joint work with Dr. Seungchan Ko (Inha University, South Korea) and Dr. Yi Yu (Guangxi University).

报告人简介：李光莲， 2015年博士毕业于得克萨斯A&M 大学，2015-2018于德国波恩大学从事Hausdorff博士后研究工作，曾获牛顿国际奖学金并于2018年前往帝国理工学院访问。2019年任挪威格罗宁根大学tenure-track助理教授，2020年任香港大学助理教授。主要从事多尺度建模与分析、不确定性量化、高维近似等研究及其在实际问题中的应用，研究工作发表于国际权威期刊SIAM系列, Journal of Computational Physics, Inverse Problems等。