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. [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. [Google Scholar]
  4. S. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 32 (2010) 2737–2764. [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). [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. [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. [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. [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. [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. [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. [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. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you