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Stochastic finite element methods for partial differential equations with random input data
16 references·16 citing·29 second hopsampled
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2017Structural Reliability Analysis and Prediction3,780 cited
  • 2016Simulation and the Monte Carlo Method3,356 cited
  • 2003Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems2,707 cited
  • 1981Simulation and the Monte Carlo Method2,402 cited
  • 1987Stochastic Simulation2,240 cited
  • 1993Optimal design of experiments1,539 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2010Numerical Methods for Stochastic Computations: A Spectral Method Approach1,107 cited
  • 2010Spectral Methods for Uncertainty Quantification953 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited

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  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • Cited by

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    • 2018Multifidelity Monte Carlo estimation for large-scale uncertainty propagation39 cited
    • 2019A Multilevel Monte Carlo Ensemble Scheme for Random Parabolic PDEs36 cited
    • 2016An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data31 cited
    • 2021An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems28 cited
    • 2015不确定性量化的高精度数值方法和理论27 cited
    • 2018Convergence analysis of multifidelity Monte Carlo estimation24 cited
    • 2018Ensemble time‐stepping algorithms for the heat equation with uncertain conductivity20 cited
    • 2017Embedded Ensemble Propagation for Improving Performance, Portability, and Scalability of Uncertainty Quantification on Emerging Computational Architectures19 cited
    • 2020Stochastic finite element method for non-linear material models16 cited
    • 2023Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling14 cited
    • 2017Comparison of approaches for random PDE optimization problems based on different matching functionals14 cited
    • 2018Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs14 cited
    • 2020A domain mapping approach for elliptic equations posed on random bulk and surface domains13 cited