SZodixStudyAcademic Library
ShelvesOpen access
Study · an open academic library·Metadata from OpenAlex (CC0)·Shelves·OpenAlex metadata, de-duplicated
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
8 references·7 citing·35 second hop
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions (2011)A Posteriori Error Analysis of Stochastic…Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)Stochastic spectral methods f…Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs (2005)Beyond Wiener–Askey Expansion…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…Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Multi-resolution analysis of …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…Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach (1999)Propagation of probabilistic …Partial Differential Equations with Random Input Data: A Perturbation Approach (2018)Partial Differential Equation…Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification (2018)Convergence of Probability De…Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations (2016)Efficient Adaptive Stochastic…Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty (2015)Error Decomposition and Adapt…A posteriori error estimation for elliptic partial differential equations with small uncertainties (2015)A posteriori error estimation…Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates (2014)Enhancing adaptive sparse gri…Propagation of Uncertainties Using Improved Surrogate Models (2013)Propagation of Uncertainties …Stochastic Finite Elements: A Spectral Approach (1991)Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos (2007)SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos (2016)Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits (2018)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. (1987)Sparse grid collocation schemes for stochastic natural convection problems (2007)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)Uncertainty propagation in CFD using polynomial chaos decomposition (2006)The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications (2008)Stochastic finite element methods for partial differential equations with random input data (2014)Numerical solution of spectral stochastic finite element systems (1996)Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2005)Long-term behavior of polynomial chaos in stochastic flow simulations (2006)Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients (2012)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Adaptive sampling-based quadrature rules for efficient Bayesian prediction (2020)A minimally invasive, efficient method for propagation of full‐field uncertainty in solid dynamics (2021)Parameter estimation with maximal updated densities (2023)A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems (2009)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces (2014)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Global sensitivity analysis using polynomial chaos expansions (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)Efficient Adaptive Algorithms for Elliptic PDEs with Random Data (2018)A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data (2020)Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations (2020)
this work references cited by second hop

References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2006Stochastic spectral methods for efficient Bayesian solution of inverse problems471 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
  • 1999Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach186 cited
  • 2005Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs153 cited

Cited by

  • 2018Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification29 cited
  • 2016Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations28 cited
  • 2013Propagation of Uncertainties Using Improved Surrogate Models19 cited
  • 2015A posteriori error estimation for elliptic partial differential equations with small uncertainties18 cited
  • 2015Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty17 cited

Only edges whose both ends are imported exist here. Widen the year window, or show the whole map. Back to the work

2014
Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates
16 cited
  • 2018Partial Differential Equations with Random Input Data: A Perturbation Approach11 cited