Journal of Scientific Computing

, Volume 68, Issue 1, pp 21–41 | Cite as

Goal-Oriented Error Estimation for the Reduced Basis Method, with Application to Sensitivity Analysis

  • Alexandre Janon
  • Maëlle Nodet
  • Clémentine Prieur


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.


Reduced basis method Surrogate model Reduced order modelling Response surface method Scientific computation Sensitivity analysis Sobol index computation Monte-Carlo method 

Mathematics Subject Classification




This work has been partially supported by the French National Research Agency (ANR) through COSINUS program (project COSTA-BRAVA nr. ANR-09-COSI-015). We thank Anthony Nouy (École Centrale de Nantes) and Yvon Maday (Université Paris 6) for fruitful discussions, and the two anonymous referees for their pertinent remarks, which have greatly improved the quality of the paper.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Alexandre Janon
    • 1
  • Maëlle Nodet
    • 2
  • Clémentine Prieur
    • 2
  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris-SudOrsayFrance
  2. 2.Laboratoire Jean KuntzmannUniversité Joseph Fourier, INRIA/MOISEGrenobleFrance

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