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

10/27/2022
by   Seungchan Ko, et al.
0

In this paper, 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-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(N^-1+δ), 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/25/2022

L^p-resolvent estimate for finite element approximation of the Stokes operator

In this paper, we will show the L^p-resolvent estimate for the finite el...
research
10/22/2019

A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty

We study an optimal control problem under uncertainty, where the target ...
research
04/26/2020

Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media

We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient...
research
07/05/2019

Exploration of a Cosine Expansion Lattice Scheme

In this article, we combine a lattice sequence from Quasi-Monte Carlo ru...
research
02/01/2023

On the numerical approximation of Blaschke-Santaló diagrams using Centroidal Voronoi Tessellations

Identifying Blaschke-Santaló diagrams is an important topic that essenti...
research
11/27/2019

Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling

When solving partial differential equations with random fields as coeffi...
research
02/17/2020

Jittering Samples using a kd-Tree Stratification

Monte Carlo sampling techniques are used to estimate high-dimensional in...

Please sign up or login with your details

Forgot password? Click here to reset