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

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 …

We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary
probability measures and apply it to solve ordinary and partial differential equations with …

In recent years, there has been a growing interest in analyzing and quantifying the effects of
random inputs in the solution of ordinary/partial differential equations. To this end, the …

Generalized polynomial chaos (gPC) has non-uniform convergence and tends to break
down for long-time integration. The reason is that the probability density distribution (PDF) of …

Uncertainty quantification through stochastic spectral methods has been recently applied to
several kinds of non-linear stochastic PDEs. In this paper, we introduce a formalism based …

Stochastic spectral methods are numerical techniques for approximating solutions to partial
differential equations with random parameters. In this work, we present and examine the …

Quantifying the uncertainty of the renewable energy generation units and loads is critical to
ensure the dynamic security of next-generation power systems. To achieve that goal, the …

We consider scalar hyperbolic conservation laws in spatial dimension $ d\geq 1$ with
stochastic initial data. We prove existence and uniqueness of a random-entropy solution and …

In recent years, extensive research has been reported about a method which is called the
generalized polynomial chaos expansion. In contrast to the sampling methods, eg, Monte …