Generalized polynomial chaos provides a reliable framework for many problems of
uncertainty quantification in computational fluid dynamics. However, it fails for long-time …

We study a dynamical large deviation principle for global solutions to the three-dimensional
Landau-Lifschitz-Navier-Stokes equations with spatially correlated noise, in a scaling …

Population dynamics models consisting of nonlinear difference equations allow us to get a
better understanding of the processes involved in epidemiology. Usually, these …

This article contributes to the development of methods for shape optimization under
uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos …

Abstract We present a Stochastic Galerkin (SG) scheme for Uncertainty Quantification (UQ)
of the compressible Navier-Stokes and Euler equations. For spatial discretization, we rely on …

In this paper, we propose a lattice Boltzmann method (LBM) for stochastic convection-
diffusion equations (CDEs). The stochastic Galerkin method is employed to transform the …

This paper concerns accurate and efficient polynomial chaos expansions (PCEs) for Asian
option pricing with uncertain volatilities. While arbitrary distributions of the volatility …

We study an incompletely parabolic system in three space dimensions with stochastic
boundary and initial data. We show how the variance of the solution can be manipulated by …

We consider a stochastic analysis of non-linear viscous fluid flow problems with smooth and
sharp gradients in stochastic space. As a representative example we consider the viscous …

The two dimensional advection–diffusion equation in a stochastically varying geometry is
considered. The varying domain is transformed into a fixed one and the numerical solution is …