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

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    Type
    Conference Paper
    Authors
    Beck, Joakim
    Nobile, F.
    Tamellini, L.
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2011-12-22
    Online Publication Date
    2011-12-22
    Print Publication Date
    2011-11
    Permanent link to this record
    http://hdl.handle.net/10754/594717
    
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    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.
    Citation
    Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients 2011, 33:10 ESAIM: Proceedings
    Publisher
    EDP Sciences
    Journal
    ESAIM: Proceedings
    DOI
    10.1051/proc/201133002
    Additional Links
    http://www.esaim-proc.org/10.1051/proc/201133002
    ae974a485f413a2113503eed53cd6c53
    10.1051/proc/201133002
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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