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A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
16 references·0 citing·32 second hop
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities (2018)A multiscale method for semi-linear ellip…To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. 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References

  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2010Adaptive sparse polynomial chaos expansion based on least angle regression1,507 cited
  • 2010Spectral Methods for Uncertainty Quantification953 cited
  • 2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2009Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations181 cited
  • 2006Numerical Methods for Differential Equations in Random Domains163 cited
  • 2006Stochastic analysis of transport in tubes with rough walls104 cited
  • 2008An extended stochastic finite element method for solving stochastic partial differential equations on random domains99 cited
  • 2007A multiscale stochastic finite element method on elliptic problems involving uncertainties99 cited
  • 2007Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method96 cited
  • 2007A fictitious domain approach to the numerical solution of PDEs in stochastic domains84 cited
  • 2008Domain decomposition of stochastic PDEs: Theoretical formulations

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65 cited
  • 2012A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties51 cited
  • 2013To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case.43 cited
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