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Stochastic galerkin and collocation methods for quantifying uncertainty in differential equations: a review
16 references·1 citing·21 second hop
Stochastic galerkin and collocation methods for quantifying uncertainty in differential equations: a review (2009)Stochastic galerkin and collocation metho…Fast Numerical Methods for Stochastic Computations: A Review (2009)Fast Numerical Methods for St…An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An Anisotropic Sparse Grid St…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Karhunen–Loève approximation of random fields by generalized fast multipole methods (2006)Karhunen–Loève approximation …High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes (2001)Convergence study of the trun…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs (2022)A bi-fidelity stochastic coll…Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)POLYNOMIAL-CHAOS-BASED KRIGING (2015)
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References

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  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
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  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
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  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques

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414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2006Karhunen–Loève approximation of random fields by generalized fast multipole methods355 cited
  • Cited by

    • 2022A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs11 cited