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SOLVING STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE EXPERIMENTAL DATA
9 references·16 citing·38 second hop
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this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2006Stochastic Differential Equations—An Introduction With Applications1,648 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 1994Numerical solution of stochastic differential equations395 cited
  • 1996Numerical solution of spectral stochastic finite element systems294 cited
  • 1999Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach186 cited
  • 1995Probabilistic Structural Mechanics Handbook173 cited
  • 1999Statistical analyses of scatterplots to identify important factors in large-scale simulations, 1: Review and comparison of techniques163 cited
  • 2017Stochastic Finite Element Method102 cited

Cited by

  • 2003A Review of Recent Developments in the Numerical Solution of Stochastic Partial Differential Equations (Stochastic Finite Elements)70 cited
  • 2007A probabilistic construction of model validation66 cited
  • 2007Reliability of computational science55 cited
  • 2012Error Analysis of a Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data44 cited
  • 2005Worst case scenario analysis for elliptic problems with uncertainty

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44 cited
  • 2017Properties of Chance Constraints in Infinite Dimensions with an Application to PDE Constrained Optimization43 cited
  • 2016Uncertainty Quantification31 cited
  • 2010A data‐driven stochastic collocation approach for uncertainty quantification in MEMS26 cited
  • 2010Weighted Smolyak algorithm for solution of stochastic differential equations on non‐uniform probability measures24 cited
  • 2012Simulation of stochastic systems via polynomial chaos expansions and convex optimization21 cited
  • 2015A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Stochastic Elliptic PDE with Constrained Control19 cited
  • 2016Stochastic Modeling and Regularity of the Nonlinear Elliptic curl--curl Equation15 cited
  • 2003ON SOLVING STOCHASTIC INITIAL-VALUE DIFFERENTIAL EQUATIONS13 cited
  • 2013Efficient computation of unsteady flow in complex river systems with uncertain inputs10 cited
  • 2007The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.10 cited
  • 2015Numerical Approximation of the Magnetoquasistatic Model with Uncertainties and its Application to Magnet Design10 cited