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The estimation of functional uncertainty using polynomial chaos and adjoint equations

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References

1991Stochastic Finite Elements: A Spectral Approach5,753 cited
2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification348 cited
2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
2006A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations335 cited
2005Stochastic Approaches to Uncertainty Quantification in CFD Simulations281 cited
2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
2007Stochastic model reduction for chaos representations191 cited
2007Probabilistic Collocation: An Efficient Non-Intrusive Approach for Arbitrarily Distributed Parametric Uncertainties

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168 cited

2003A Stochastic Collocation Algorithm for Uncertainty Analysis148 cited

2000Efficient Sensitivity/Uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems105 cited

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