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A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient

Abstract : In this work, a Reduced Basis (RB) approach is used to solve a large number of Boundary Value Problems (BVPs) parametrized by a stochastic input — expressed as a Karhunen-Loève expansion — in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for “statistical” outputs — such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.
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https://hal.inria.fr/inria-00311463
Contributor : Sébastien Boyaval <>
Submitted on : Monday, August 18, 2008 - 11:44:59 AM
Last modification on : Friday, March 27, 2020 - 3:45:34 AM
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  • HAL Id : inria-00311463, version 1

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Sébastien Boyaval, Claude Le Bris, Yvon Maday, Ngoc Cuong Nguyen, Anthony Patera. A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient. [Research Report] RR-6617, INRIA. 2008, pp.50. ⟨inria-00311463⟩

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