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 香港大学数学系
时间：2323年7月23日3:00（下午）
报告形式：线上报告（腾讯会议）
腾讯会议号： 591 802 537
邀请人：李秋齐
报告摘要：In this talk, we analyze the numerical approximation of the Navier–Stokes problem over a bounded polygonal domain in 
, 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–Loéve 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 O(), where N is the number of sampling points, δ > 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 Seungchan Ko (Inha University, Incheon,Republic of Korea) and Yi Yu (Guangxi University, Nanning, Guangxi, PRChina).
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。
