Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
ESAIM. Proceedings, Tome 33 (2011), pp. 10-21
Cet article a éte moissonné depuis la source EDP Sciences
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.
Affiliations des auteurs :
J. Beck 1 ; F. Nobile 2 ; L. Tamellini 2 ; R. Tempone 1
@article{EP_2011_33_a2,
author = {J. Beck and F. Nobile and L. Tamellini and R. Tempone},
title = {Implementation of optimal {Galerkin} and {Collocation} approximations of {PDEs} with {Random} {Coefficients}},
journal = {ESAIM. Proceedings},
pages = {10--21},
year = {2011},
volume = {33},
doi = {10.1051/proc/201133002},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201133002/}
}
TY - JOUR AU - J. Beck AU - F. Nobile AU - L. Tamellini AU - R. Tempone TI - Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients JO - ESAIM. Proceedings PY - 2011 SP - 10 EP - 21 VL - 33 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201133002/ DO - 10.1051/proc/201133002 LA - en ID - EP_2011_33_a2 ER -
%0 Journal Article %A J. Beck %A F. Nobile %A L. Tamellini %A R. Tempone %T Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients %J ESAIM. Proceedings %D 2011 %P 10-21 %V 33 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201133002/ %R 10.1051/proc/201133002 %G en %F EP_2011_33_a2
J. Beck; F. Nobile; L. Tamellini; R. Tempone. Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients. ESAIM. Proceedings, Tome 33 (2011), pp. 10-21. doi: 10.1051/proc/201133002
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