Open Access
Issue
ESAIM: M2AN
Volume 52, Number 2, March–April 2018
Page(s) 705 - 728
DOI https://doi.org/10.1051/m2an/2018003
Published online 11 July 2018
  1. M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. Acad. Sci. Paris 339 (2004) 667–672. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. (2001) 10 1–102. [CrossRef] [MathSciNet] [Google Scholar]
  3. T. Bui-Thanh, K. Willcox, O. Ghattas and B. van Bloemen Waanders, Goal-oriented, model-constrained optimization for reduction of large-scale systems. J. Comput. Phys. 224 (2007) 880–896. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 32 (2010) 2737–2764. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Drohmann and K. Carlberg, The ROMES method for statistical modeling of reduced-order-model error. SIAM/ASA J. Uncertain. Quantif. 3 (2015) 116–145. [CrossRef] [Google Scholar]
  6. R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, New York (1991). [CrossRef] [Google Scholar]
  7. M. Ilak and C. Rowley, Modeling of transitional channel flow using balanced proper orthogonal decomposition. Phys. Fluids 20 (2008) 034103. [CrossRef] [Google Scholar]
  8. A. Janon, M. Nodet and C. Prieur, Certified reduced-basis solutions of viscous Burgers equations parametrized by initial and boundary values. ESAIM: M2AN 47 (2013) 317–348. [CrossRef] [EDP Sciences] [Google Scholar]
  9. A. Janon, M. Nodet and C. Prieur, Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis. J. Sci. Comput. 68 (2016) 21–41. [CrossRef] [Google Scholar]
  10. A. Janon, M. Nodet, C. Prieur and C. Prieur, Global sensitivity analysis for the boundary control of an open channel. Math. Control Signals Syst. 28 (2016) 1–27. [CrossRef] [Google Scholar]
  11. J. Kleijnen, Design and Analysis of Simulation Experiments. Springer Publishing Company, Inc. (2007). [Google Scholar]
  12. J. Kleijnen, Simulation experiments in practice: statistical design and regression analysis. J. Simul. 2 (2008) 19–27. [CrossRef] [Google Scholar]
  13. O.P. Le Maître, O.M. Knio, B.J. Debusschere, H.N. Najm and R.G. Ghanem, A multigrid solver for two-dimensional stochastic diffusion equations. Comput. Methods Appl. Mech. Eng. 192 (2003) 4723–4744. [CrossRef] [Google Scholar]
  14. Y. Maday, A. Patera and D. Rovas, A blackbox reduced-basis output bound method for noncoercive linear problems, in Nonlinear Partial Differential Equations and their Applications Collège de France Seminar Volume XIV, edited by D. Cioranescu and J.-L. Lions. Vol. 31 of Studies in Mathematics and Its Applications. Elsevier (2002) 533–569. [CrossRef] [Google Scholar]
  15. B. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control 26 (1981) 17–31. [CrossRef] [MathSciNet] [Google Scholar]
  16. N. Nguyen, K. Veroy and A. Patera, Certified real-time solution of parametrized partial differential equations, in Handbook of Materials Modeling. Springer (2005) 1523–1558. [Google Scholar]
  17. N. Nguyen, G. Rozza and A. Patera, Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Calcolo 46 (2009) 157–185. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Nouy, Low-Rank Tensor Methods for Model Order Reduction. To appear in: Handbook of Uncertainty Quantification (2016) 1–26. DOI:10.1007/978-3-319-11259-6_21-1 [Google Scholar]
  19. T. Santner, B. Williams and W. Notz, The Design and Analysis of Computer Experiments. Springer-Verlag, New York (2003) 283. [Google Scholar]
  20. J.M.A. Scherpen and W.S. Gray, Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis. Nonlinear Anal. 51 (2002) 883–901. [CrossRef] [Google Scholar]
  21. M. Scheuerer, R. Schaback and M. Schlather, Interpolation of spatial data – a stochastic or a deterministic problem? Eur. J. Appl. Math. 24 (2013) 601–629. [CrossRef] [Google Scholar]
  22. L. Sirovich, Turbulence and the dynamics of coherent structures. Part I & II. Quart. Appl. Math. 45 (1987) 561–590. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  23. C. Soize and R. Ghanem, Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J. Sci. Comput. 26 (2004) 395–410. [CrossRef] [MathSciNet] [Google Scholar]
  24. K. Veroy, C. Prud’homme and A. Patera, Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds. C. R. Math. Acad. Sci. Paris 337 (2003) 619–624. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Volkwein, Proper Orthogonal Decomposition and Singular Value Decomposition. Spezialforschungsbereich F003 Optimierung und Kontrolle, Projektbereich Kontinuierliche Optimierung und Kontrolle, Bericht. Nr. 153, Graz (1999). [Google Scholar]
  26. K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition. AIAA J. 40 (2002) 2323–2330. [CrossRef] [Google Scholar]
  27. M. Yano and A.T. Patera, A space–time variational approach to hydrodynamic stability theory, in Vol. 469 of Proc. R. Soc. A. The Royal Society (2013) 20130036. [CrossRef] [Google Scholar]
  28. M. Yano, A.T. Patera and K. Urban, A space-time hp-interpolation-based certified reduced basis method for Burgers’ equation. Math. Model. Methods Appl. Sci. 24 (2014) 1903–1935. [CrossRef] [Google Scholar]
  29. D. Zupanski and M. Zupanski, Model error estimation employing an ensemble data assimilation approach. Mon. Weather Rev. 134 (2006) 1337–1354. [CrossRef] [Google Scholar]

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