Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2011-12-22Online Publication Date
2011-12-22Print Publication Date
2011-11Permanent link to this record
http://hdl.handle.net/10754/594717
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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: ProceedingsPublisher
EDP SciencesJournal
ESAIM: ProceedingsAdditional Links
http://www.esaim-proc.org/10.1051/proc/201133002ae974a485f413a2113503eed53cd6c53
10.1051/proc/201133002