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Finite elements for stochastic media problems
8 references·16 citing·37 second hop
Finite elements for stochastic media problems (1999)Finite elements for stochastic media prob…Stochastic partial differential equations (2020)Stochastic partial differenti…Numerical solution of stochastic differential equations (2016)Numerical solution of stochas…Stochastic Differential Equations (2003)Stochastic Differential Equat…Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements (1997)Uncertainties in probabilisti…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Computational Mechanics of Probabilistic and Reliability Analysis (1991)Computational Mechanics of Pr…Adaptive sampling — an iterative fast Monte Carlo procedure (1988)Adaptive sampling — an iterat…Random Fields: Analysis and Synthesis (1983)Random Fields: Analysis and S…Reduced Wiener Chaos representation of random fields via basis adaptation and projection (2017)Reduced Wiener Chaos represen…To be or not to be intrusive? 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this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2016Numerical solution of stochastic differential equations5,001 cited
  • 2003Stochastic Differential Equations2,978 cited
  • 1983Random Fields: Analysis and Synthesis1,302 cited
  • 1988Adaptive sampling — an iterative fast Monte Carlo procedure464 cited
  • 1997Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements354 cited
  • 2020Stochastic partial differential equations216 cited
  • 1991Computational Mechanics of Probabilistic and Reliability Analysis95 cited

Cited by

  • 2007QUANTIFYING UNCERTAINTY: MODERN COMPUTATIONAL REPRESENTATION OF PROBABILITY AND APPLICATIONS77 cited
  • 2012Sampling-free linear Bayesian update of polynomial chaos representations75 cited
  • 2003A multigrid solver for two-dimensional stochastic diffusion equations74 cited
  • 2003A Review of Recent Developments in the Numerical Solution of Stochastic Partial Differential Equations (Stochastic Finite Elements)70 cited
  • 2004Uncertainty Quantification with Stochastic Finite Elements70 cited
  • 2004Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering69 cited

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2004
Supersensitivity due to uncertain boundary conditions
64 cited
  • 2003Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations61 cited
  • 2000Transient Dynamics of Stochastically Parametered Beams51 cited
  • 2017Reduced Wiener Chaos representation of random fields via basis adaptation and projection48 cited
  • 2013To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case.43 cited
  • 2004Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation43 cited
  • 2007A Fourier–Karhunen–Loève discretization scheme for stationary random material properties in SFEM41 cited
  • 2003Solving stochastic heat transfer problems39 cited
  • 2013Karhunen–Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis.37 cited
  • 2011Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System37 cited