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Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
14 references·16 citing·22 second hop
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References

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  • 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
  • 2008The stochastic finite element method: Past, present and future999 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
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2004Finite elements for elliptic problems with stochastic coefficients364 cited
  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
  • 2006Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

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Cited by

  • 2012ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS136 cited
  • 2013Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations129 cited
  • 2012Stochastic Modeling-Based Variability Analysis of On-Chip Interconnects96 cited
  • 2012Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model89 cited
  • 2010ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA81 cited
  • 2011Optimal control with stochastic PDE constraints and uncertain controls73 cited
  • 2016Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations65 cited
  • 2013Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients64 cited
  • 2015Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format63 cited
  • 2016Multi-Index Stochastic Collocation for random PDEs59 cited
  • 2018Large deformation shape uncertainty quantification in acoustic scattering51 cited
  • 2015A Multi Level Monte Carlo method with control variate for elliptic PDEs with log-normal coefficients46 cited
  • 2015Fast Bayesian optimal experimental design for seismic source inversion46 cited
  • 2018Basis adaptive sample efficient polynomial chaos (BASE-PC)42 cited
  • 2013Variability Analysis of Interconnects Terminated by General Nonlinear Loads41 cited
  • 2017A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases38 cited