Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis

Alexandre Janon 1, 2 Maëlle Nodet 1, 3 Clémentine Prieur 1, 3
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear functional of the PDE solution. A new probabilistic error bound for the reduced model is proposed. It is efficiently and explicitly computable, and we show on different examples that this error bound is sharper than existing ones. We include application of our work to sensitivity analysis studies.
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Submitted on : Thursday, July 10, 2014 - 7:13:01 PM
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Alexandre Janon, Maëlle Nodet, Clémentine Prieur. Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis. Journal of Scientific Computing, Springer Verlag, 2016, 68 (1), pp.21-41. ⟨10.1007/s10915-015-0127-z⟩. ⟨hal-00721616v3⟩

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