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Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
11 references·16 citing·25 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 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
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2004Finite elements for elliptic problems with stochastic coefficients364 cited
  • 2013Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods187 cited
  • 1999Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach186 cited

Cited by

  • 2015A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data109 cited
  • 2011Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem93 cited

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  • 2016Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations65 cited
  • 2016Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients64 cited
  • 2013N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS58 cited
  • 2012A stochastic collocation method for the second order wave equation with a discontinuous random speed58 cited
  • 2017Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients48 cited
  • 2014Random field representations for stochastic elliptic boundary value problems and statistical inverse problems36 cited
  • 2017Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients34 cited
  • 2014On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification33 cited
  • 2016Uncertainty Quantification31 cited
  • 2016Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients30 cited
  • 2015Analysis and computation of the elastic wave equation with random coefficients28 cited
  • 2016Multilevel Accelerated Quadrature for PDEs with Log-Normally Distributed Diffusion Coefficient28 cited
  • 2013The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem27 cited
  • 2015不确定性量化的高精度数值方法和理论27 cited