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Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
6 references·16 citing·24 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
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited

Cited by

  • 2012Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion451 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data400 cited
  • 2008A comparative study of uncertainty propagation methods for black-box-type problems331 cited
  • 2008The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications214 cited
  • 2009Multi-element probabilistic collocation method in high dimensions203 cited
  • 2008Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos187 cited

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2010
Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems
183 cited
  • 2009Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations181 cited
  • 2008Uncertainty quantification for systems of conservation laws177 cited
  • 2010Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison176 cited
  • 2006Long-term behavior of polynomial chaos in stochastic flow simulations173 cited
  • 2011Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances161 cited
  • 2008Sparse high order FEM for elliptic sPDEs137 cited
  • 2010Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems127 cited
  • 2018Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits121 cited