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N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS
15 references·6 citing·27 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 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
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2010Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs306 cited
  • 2011Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients296 cited
  • 2011Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs260 cited
  • 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
  • 2011Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications160 cited
  • 2012Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients154 cited
  • 2012

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ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
136 cited
  • 2009STOCHASTIC GALERKIN DISCRETIZATION OF THE LOG-NORMAL ISOTROPIC DIFFUSION PROBLEM68 cited
  • Cited by

    • 2017Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients34 cited
    • 2017Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs32 cited
    • 2013A Quasi-optimal Sparse Grids Procedure for Groundwater Flows16 cited
    • 2020Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations13 cited
    • 2024Stochastic modelling of symmetric positive definite material tensors12 cited
    • 2022On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion11 cited