The current interest in the combustion chemistry of hydrocarbon fuels, including the various
alcohol and biodiesel compounds, motivates this review of the methods and application of …

The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a
significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) …

The paper describes the philosophy, design, functionality, and usage of the Python software
toolbox Chaospy for performing uncertainty quantification via polynomial chaos expansions …

Discrepancies frequently occur between a physical system's responses and predictions
obtained from mathematical models. The Spectral Stochastic Finite Element Method …

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to
represent the random model response by a set of coefficients in a suitable (so-called …

This paper presents a review of the current state-of-the-art of numerical methods for
stochastic computations. The focus is on efficient high-order methods suitable for practical …

A number of approaches for discretizing partial differential equations with random data are
based on generalized polynomial chaos expansions of random variables. These constitute …

The basic random variables on which random uncertainties can in a given model depend
can be viewed as defining a measure space with respect to which the solution to the …

Stationary systems modelled by elliptic partial differential equations—linear as well as
nonlinear—with stochastic coefficients (random fields) are considered. The mathematical …

We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic
partial differential equations subject to uncertain inputs. In particular, we focus on the …