Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
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Propagation of combined parametric and nonparametric uncertainties in elliptic partial differential equations is considered. Two cases, namely, (a) both uncertainties are over the entire domain, and (b) different types of uncertainties are over non-overlapping subdomains are proposed. Parametric uncertainty is modelled by a random field and is discretised using the Karhunen-Loeve (KL) expansion. The nonparametric uncertainty is modelled by Wishart random matrix. Both uncertainties are considered independent, and the two first moments of the response are calculated using polynomial chaos expansion and analytical random matrix theory results. Closed-form analytical expressions of the first two moments are derived for both cases.