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Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems
15 references·9 citing·29 second hop
Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems (2010)Solution verification, goal-oriented adap…Fast Numerical Methods for Stochastic Computations: A Review (2009)Fast Numerical Methods for St…Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients (2009)Analysis and implementation i…Sparse high order FEM for elliptic sPDEs (2008)Sparse high order FEM for ell…Efficient stochastic Galerkin methods for random diffusion equations (2008)Efficient stochastic Galerkin…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…Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network (2007)Parametric uncertainty analys…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…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…An efficient method for parametric uncertainty analysis of numerical geophysical models (1997)An efficient method for param…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data (2020)A fully adaptive multilevel s…Partial Differential Equations with Random Input Data: A Perturbation Approach (2018)Partial Differential Equation…Goal-oriented adaptive surrogate construction for stochastic inversion (2018)Goal-oriented adaptive surrog…A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method (2018)A Posteriori Error Estimation…Enhanced goal‐oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems (2016)Enhanced goal‐oriented error …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…Propagation of Uncertainties Using Improved Surrogate Models (2013)Propagation of Uncertainties …Convergence Rates of Multilevel and Sparse Tensor Approximations for a Random Elliptic PDE (2013)Convergence Rates of Multilev…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)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)The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. 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References

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  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
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  • 2008Efficient stochastic Galerkin methods for random diffusion equations90 cited
  • 2007Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

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89 cited
  • 2009Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients88 cited
  • Cited by

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    • 2015Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty17 cited
    • 2013Convergence Rates of Multilevel and Sparse Tensor Approximations for a Random Elliptic PDE17 cited
    • 2020A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data14 cited
    • 2018Goal-oriented adaptive surrogate construction for stochastic inversion13 cited
    • 2018Partial Differential Equations with Random Input Data: A Perturbation Approach11 cited
    • 2016Enhanced goal‐oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems7 cited