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Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces
6 references·16 citing·35 second hop
Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces (2013)Approximation of Quantities of Interest i…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)Point-Collocation Nonintrusiv…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A Stochastic Collocation Meth…Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach (2008)Sparse polynomial chaos expan…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Robust adaptive least squares polynomial chaos expansions in high‐frequency applications (2023)Robust adaptive least squares…Robust adaptive least squares polynomial chaos expansions in high‐frequency applications (2020)Robust adaptive least squares…Polynomial chaos expansions for dependent random variables (2019)Polynomial chaos expansions f…On the merits of sparse surrogates for global sensitivity analysis of multi-scale nonlinear problems: Application to turbulence and fire-spotting model in wildland fire simulators (2019)On the merits of sparse surro…Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation (2018)Review and comparison of two …Projection methods for stochastic dynamic systems: A frequency domain approach (2018)Projection methods for stocha…ASSESSING THE PERFORMANCE OF LEJA AND CLENSHAW-CURTIS COLLOCATION FOR COMPUTATIONAL ELECTROMAGNETICS WITH RANDOM INPUT DATA (2018)ASSESSING THE PERFORMANCE OF …Affordable Uncertainty Quantification for Industrial Problems: Application to Aero-Engine Fans (2018)Affordable Uncertainty Quanti…Stochastic Collocation Methods: A Survey (2017)Stochastic Collocation Method…Polynomial Surrogates for Open-Channel Flows in Random Steady State (2017)Polynomial Surrogates for Ope…Effectively Subsampled Quadratures for Least Squares Polynomial Approximations (2017)Effectively Subsampled Quadra…On polynomial chaos expansion via gradient-enhanced ℓ1-minimization (2016)On polynomial chaos expansion…Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression (2016)Nonadaptive Quasi-Optimal Poi…Stochastic Collocation Methods: A Survey (2015)Stochastic Collocation Method…To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. 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this work references cited by second hop

References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data400 cited
  • 2008Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach270 cited
  • 2010Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics244 cited

Cited by

  • 2019Polynomial chaos expansions for dependent random variables80 cited
  • 2016On polynomial chaos expansion via gradient-enhanced ℓ1-minimization72 cited
  • 2016Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression60 cited
  • 2017Effectively Subsampled Quadratures for Least Squares Polynomial Approximations43 cited
  • 2013To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case.43 cited
  • 2018Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation40 cited
  • 2018Affordable Uncertainty Quantification for Industrial Problems: Application to Aero-Engine Fans36 cited

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  • 2017Stochastic Collocation Methods: A Survey27 cited
  • 2019On the merits of sparse surrogates for global sensitivity analysis of multi-scale nonlinear problems: Application to turbulence and fire-spotting model in wildland fire simulators24 cited
  • 2018ASSESSING THE PERFORMANCE OF LEJA AND CLENSHAW-CURTIS COLLOCATION FOR COMPUTATIONAL ELECTROMAGNETICS WITH RANDOM INPUT DATA23 cited
  • 2023Robust adaptive least squares polynomial chaos expansions in high‐frequency applications18 cited
  • 2017Polynomial Surrogates for Open-Channel Flows in Random Steady State17 cited
  • 2013A Quasi-optimal Sparse Grids Procedure for Groundwater Flows16 cited
  • 2018Projection methods for stochastic dynamic systems: A frequency domain approach16 cited
  • 2020Robust adaptive least squares polynomial chaos expansions in high‐frequency applications16 cited
  • 2015Stochastic Collocation Methods: A Survey12 cited