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A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
16 references·3 citing·28 second hop
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data (2020)A fully adaptive multilevel stochastic co…Multi-fidelity stochastic collocation method for computation of statistical moments (2017)Multi-fidelity stochastic col…Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs (2017)Fully Discrete Approximation …A Multilevel Monte Carlo Method for Computing Failure Probabilities (2016)A Multilevel Monte Carlo Meth…A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2015)A Multilevel Stochastic Collo…Adaptive stochastic Galerkin FEM (2013)Adaptive stochastic Galerkin …Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011)Multilevel Monte Carlo method…Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Multi-level Monte Carlo Finit…Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison (2010)Stochastic Spectral Galerkin …Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems (2010)Solution verification, goal-o…An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…Multilevel Monte Carlo Path Simulation (2008)Multilevel Monte Carlo Path S…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…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Numerical Methods for Differential Equations in Random Domains (2006)Numerical Methods for Differe…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Context-Aware Surrogate Modeling for Balancing Approximation and Sampling Costs in Multifidelity Importance Sampling and Bayesian Inverse Problems (2023)Context-Aware Surrogate Model…On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion (2022)On the Convergence of Adaptiv…Convergence of adaptive stochastic collocation with finite elements (2021)Convergence of adaptive stoch…Stochastic Finite Elements: A Spectral Approach (1991)Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)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)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)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)Stochastic Differential Equations: An Introduction with Applications. 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39 cited
  • 2010Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems34 cited
  • 2017Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs32 cited
  • Cited by

    • 2023Context-Aware Surrogate Modeling for Balancing Approximation and Sampling Costs in Multifidelity Importance Sampling and Bayesian Inverse Problems14 cited
    • 2022On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion11 cited
    • 2021Convergence of adaptive stochastic collocation with finite elements9 cited