Nonparametric Density Estimation for Randomly Perturbed Elliptic Problems I: Computational Methods, A Posteriori Analysis, and Adaptive Error Control

@article{Estep2009NonparametricDE,
  title={Nonparametric Density Estimation for Randomly Perturbed Elliptic Problems I: Computational Methods, A Posteriori Analysis, and Adaptive Error Control},
  author={Donald J. Estep and Axel M{\aa}lqvist and Simon Tavener},
  journal={SIAM J. Scientific Computing},
  year={2009},
  volume={31},
  pages={2935-2959}
}
We consider the nonparametric density estimation problem for a quantity of interest computed from solutions of an elliptic partial differential equation with randomly perturbed coefficients and data. Our particular interest are problems for which limited knowledge of the random perturbations are known. We derive an efficient method for computing samples and generating an approximate probability distribution based on Lion’s domain decomposition method and the Neumann series. We then derive an a… CONTINUE READING
Highly Cited
This paper has 21 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 13 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 16 references

Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems

  • M. G. Larson, A. Målqvist
  • Comput. Methods Appl. Mech. Engrg., 196
  • 2007

Solving elliptic boundary value problems with uncertain coefficients by the finite element method : The stochastic formulation , Comput

  • R. Tempone I. Babuška, G. E. Zouraris
  • Methods Appl . Mech . Engrg .
  • 2005

Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation

  • I. Babuška, R. Tempone, G. E. Zouraris
  • Comput. Methods Appl. Mech. Engrg., 194
  • 2005
1 Excerpt

Stochastic Finite Elements: A Spectral Approach

  • R. Ghanem, P. Spanos
  • Dover, New York
  • 2003
1 Excerpt

Upscaling : a review , Internat

  • C. L. Farmer
  • J . Numer . Methods Fluids
  • 2002

Upscaling: a review

  • C. L. Farmer
  • Internat. J. Numer. Methods Fluids, 40 (2002), pp…
  • 2001
1 Excerpt

Similar Papers

Loading similar papers…