Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
On the Gibbs Phenomenon and Its Resolution
SIAM Review
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Towards the resolution of the Gibbs phenomena
Journal of Computational and Applied Mathematics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Time-dependent generalized polynomial chaos
Journal of Computational Physics
Orthogonal functionals of the Poisson process
IEEE Transactions on Information Theory
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In this paper, we propose a new iterative formulation improving the convergence of standard non intrusive stochastic spectral method for uncertainty quantification. We demonstrate that the method is more accurate than the classical approach with the same level of approximation and at no significant additional computational or memory cost, since it is deployed in a post-processing stage. Moreover, the accuracy of the representation improves no matter the regularity of the random quantity of interest. Therefore, the method is particularly well suited when nonlinear transformations of random variables are in play and can be viewed as a new way of tackling the Gibbs phenomenon. We apply the method to several test cases with different levels of regularity, dimensionality and complexity, including the case of compressible gas dynamics and long time-integration problems. The new and the classical approaches are compared for the resolution of a stochastic Riemann problem governed by an Euler system.