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

报告时间：2023-09-19   19:00-20:00

报告人：A.Prof. Guanglian Li ,The University of Hong Kong

报告地点：理学院东北楼四楼报告厅（404）

Abstract: In this talk, we analyze the numerical approximation of the Navier–Stokes problem over a bounded polygonal domain in R2, where the initial condi- tionis 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´eveexpansion 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(N−1+δ), where N is the number of sam- pling points, δ > 0 is an arbitrary small number, and the constant in the decay estimate is independent of the dimension of integration. This is the first rigorous theoretical analysis of QMC sampling strategy for the nonlinear problem. This is a joint work with Seungchan Ko (InhaUniversity, Incheon, Republic of Korea) and Yi Yu (Guangxi University, Nanning, Guangxi, PR China).