This work presents an h p-adaptive variant of multi-element polynomial chaos expansion
(ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME …

Since Kolmogorov's theory, turbulence has been studied using various methods, many of
which could be now be understood in a probabilistic framework. Herein, a comprehensive …

This article is devoted to providing a review of mathematical formulations in which
Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive …

Parametric uncertainty in a dynamical system has the potential to undermine the
performance of a closed-loop controller designed through classical techniques. This paper …

For the investigation of uncertainties in high dimensional spaces of computationally
expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are …

Generalized polynomial chaos (gPC), often combined with mono-implicit Runge--Kutta
(MIRK) methods, is widely used to solve random ODEs. We investigate the impact of …

We study the time-dependent Navier–Stokes equations in the context of stochastic finite
element discretizations. Specifically, we assume that the viscosity is a random field given in …

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

This work presents a comprehensive framework for the sensitivity analysis of the Navier–
Stokes equations, with an emphasis on the stability estimate of the discretized first‐order …

We consider the numerical approximation of different ordinary differential equations (ODEs)
and partial differential equations (PDEs) with periodic boundary conditions involving a one …