The stochastic finite element method: past, present and future

G Stefanou - Computer methods in applied mechanics and …, 2009 - Elsevier
A powerful tool in computational stochastic mechanics is the stochastic finite element
method (SFEM). SFEM is an extension of the classical deterministic FE approach to the …

Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics

HN Najm - Annual review of fluid mechanics, 2009 - annualreviews.org
The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a
significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) …
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H Harbrecht, M Peters, M Siebenmorgen - Numerische Mathematik, 2016 - Springer
In this article, we provide a rigorous analysis of the solution to elliptic diffusion problems on
random domains. In particular, based on the decay of the Karhunen-Loève expansion of the …

Effective pore‐scale dispersion upscaling with a correlated continuous time random walk approach

T Le Borgne, D Bolster, M Dentz… - Water Resources …, 2011 - Wiley Online Library
We investigate the upscaling of dispersion from a pore‐scale analysis of Lagrangian
velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of …

An extended stochastic finite element method for solving stochastic partial differential equations on random domains

A Nouy, A Clement, F Schoefs, N Moes - Computer Methods in Applied …, 2008 - Elsevier
Recently, a new strategy was proposed to solve stochastic partial differential equations on
random domains. It is based on the extension to the stochastic framework of the extended …

Large deformation shape uncertainty quantification in acoustic scattering

R Hiptmair, L Scarabosio, C Schillings… - Advances in …, 2018 - Springer
We address shape uncertainty quantification for the two-dimensional Helmholtz
transmission problem, where the shape of the scatterer is the only source of uncertainty. In …

[HTML][HTML] Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

JE Castrillon-Candas, F Nobile, RF Tempone - Computers & Mathematics …, 2016 - Elsevier
In this work we consider the problem of approximating the statistics of a given Quantity of
Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random …