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Analysis of the domain mapping method for elliptic diffusion problems on random domains
10 references·6 citing·27 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2006Karhunen–Loève approximation of random fields by generalized fast multipole methods355 cited
  • 2010Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs306 cited
  • 2006Numerical Methods for Differential Equations in Random Domains163 cited
  • 2012ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS136 cited
  • 2008Sparse second moment analysis for elliptic problems in stochastic domains122 cited
  • 2006Stochastic analysis of transport in tubes with rough walls104 cited
  • 2007A fictitious domain approach to the numerical solution of PDEs in stochastic domains84 cited
  • 2016Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations65 cited

Cited by

  • 2018Large deformation shape uncertainty quantification in acoustic scattering51 cited
  • 2022A stochastic finite element scheme for solving partial differential equations defined on random domains26 cited
  • 2020Domain Uncertainty Quantification in Computational Electromagnetics22 cited
  • 2021A Bayesian approach for quantile optimization problems with high-dimensional uncertainty sources

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17 cited
  • 2020A domain mapping approach for elliptic equations posed on random bulk and surface domains13 cited
  • 2024On Uncertainty Quantification of Eigenvalues and Eigenspaces with Higher Multiplicity10 cited