Intrusive and Non-Intrusive Polynomial Chaos Approximations for a Two-Dimensional Steady State Navier-Stokes System with Random Forcing

TL;DR

This paper explores the convergence of polynomial chaos methods applied to a two-dimensional steady-state Navier-Stokes system with random forcing, focusing on the challenges posed by non-linear equations.

Contribution

It provides new insights into the convergence behavior of polynomial chaos approximations for non-linear PDEs, specifically the Navier-Stokes equations with quadratic nonlinearity.

Findings

Convergence properties are characterized for the non-linear Navier-Stokes system.

The study identifies conditions under which polynomial chaos approximations are effective.

Results highlight differences between linear and non-linear equation approximations.

Abstract

While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this convergence for a particular equation with quadratic nonlinearity.