Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆

Beck, J., et al. Dobrzynski, Cécile, Colin, Thierry, and Abgrall, Rémi, eds. "Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆." ESAIM: Proceedings 33 (2011): 10-21. <http://eudml.org/doc/251288>.

@article{Beck2011,
abstract = {In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. },
author = {Beck, J., Nobile, F., Tamellini, L., Tempone, R.},
editor = {Dobrzynski, Cécile, Colin, Thierry, Abgrall, Rémi},
journal = {ESAIM: Proceedings},
keywords = {Uncertainty Quantification; PDEs with random data; elliptic equations; multivariate polynomial approximation; Best M-Terms approximation; Stochastic Galerkin methods; Smolyak approximation; Sparse grids, Stochastic Collocation methods; uncertainty quantification; best -terms approximation; stochastic Galerkin methods; sparse grids; stochastic collocation methods},
language = {eng},
month = {12},
pages = {10-21},
publisher = {EDP Sciences},
title = {Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆},
url = {http://eudml.org/doc/251288},
volume = {33},
year = {2011},
}

TY - JOUR
AU - Beck, J.
AU - Nobile, F.
AU - Tamellini, L.
AU - Tempone, R.
AU - Dobrzynski, Cécile
AU - Colin, Thierry
AU - Abgrall, Rémi
TI - Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆
JO - ESAIM: Proceedings
DA - 2011/12//
PB - EDP Sciences
VL - 33
SP - 10
EP - 21
AB - In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.
LA - eng
KW - Uncertainty Quantification; PDEs with random data; elliptic equations; multivariate polynomial approximation; Best M-Terms approximation; Stochastic Galerkin methods; Smolyak approximation; Sparse grids, Stochastic Collocation methods; uncertainty quantification; best -terms approximation; stochastic Galerkin methods; sparse grids; stochastic collocation methods
UR - http://eudml.org/doc/251288
ER -