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Non-intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities
9 references·5 citing·30 second hop
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 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
  • 1975Providence, Rhode Island626 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2005Stochastic Approaches to Uncertainty Quantification in CFD Simulations281 cited
  • 1995Direct incorporation of uncertainty in chemical and environmental engineering systems147 cited
  • 2009Stochastic Finite Elements113 cited
  • 2014Stochastic Finite Elements52 cited

Cited by

  • 2022DYNAMICAL LOW-RANK APPROXIMATION FOR BURGERS' EQUATION WITH UNCERTAINTY18 cited
  • 2020Intrusive acceleration strategies for uncertainty quantification for hyperbolic systems of conservation laws15 cited
  • 2018A non-intrusive B-splines Bézier elements-based method for uncertainty propagation13 cited
  • 2016An Overview of Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations13 cited
  • 2019Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

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12 cited