Free Access
Volume 48, Number 4, July-August 2014
Page(s) 943 - 953
Published online 30 June 2014
  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. Anal. Numér. 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 Numerica 10 (2001) 1–102. [Google Scholar]
  3. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43 (2011) 1457–1472. [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. P. Chen and A. Quarteroni, Accurate and efficient evaluation of failure probability for partial differential equations with random input data. Comput. Methods Appl. Mech. Eng. 267 (2013) 233–260. [CrossRef] [Google Scholar]
  6. P. Chen, A. Quarteroni and G. Rozza, Comparison between reduced basis and stochastic collocation methods for elliptic problems. J. Sci. Comput. 59 (2014) 187–216. [CrossRef] [Google Scholar]
  7. P. Chen, A. Quarteroni and G. Rozza, A weighted reduced basis method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 51 (2013) 3163–3185. [Google Scholar]
  8. R.A. DeVore and G.G. Lorentz, Constructive Approximation. Springer (1993). [Google Scholar]
  9. M.B. Giles and E. Süli, Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica 11 (2002) 145–236. [CrossRef] [MathSciNet] [Google Scholar]
  10. M.A. Grepl, Y. Maday, N.C. Nguyen and A.T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. ESAIM: M2AN 41 (2007) 575–605. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. T. Lassila, A. Manzoni and G. Rozza, On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition. ESAIM: M2AN 46 (2012) 1555–1576. [CrossRef] [EDP Sciences] [Google Scholar]
  12. T. Lassila and G. Rozza, Parametric free-form shape design with PDE models and reduced basis method. Comput. Methods Appl. Mech. Eng. 199 (2010) 1583–1592. [Google Scholar]
  13. Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383–404. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Manzoni, A. Quarteroni and G. Rozza, Model reduction techniques for fast blood flow simulation in parametrized geometries. Int. J. Numer. Methods Biomedical Eng. 28 (2012) 604–625. [Google Scholar]
  15. F. Nobile, R. Tempone and C.G. Webster, A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. 46 (2008) 2309–2345. [CrossRef] [MathSciNet] [Google Scholar]
  16. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications. Springer (2010). [Google Scholar]
  17. A. Pinkus, N-widths in Approximation Theory. Springer (1985). [Google Scholar]
  18. A. Quarteroni, G. Rozza and A. Manzoni, Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Industry 1 (2011) 1–49. [Google Scholar]
  19. A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics. Springer (2007). [Google Scholar]
  20. G. Rozza, Reduced basis methods for Stokes equations in domains with non-affine parameter dependence. Comput. Vis. Sci. 12 (2009) 23–35. [CrossRef] [Google Scholar]
  21. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives Comput. Meth. Eng. 15 (2008) 229–275. [Google Scholar]
  22. K. Urban and B. Wieland, Affine decompositions of parametric stochastic processes for application within reduced basis methods. In Proc. MATHMOD, 7th Vienna International Conference on Mathematical Modelling (2012). [Google Scholar]

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