- M. Barrault, N.C. Nguyen, Y. Maday and A.T. Patera. An empirical interpolation method: Application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris Ser. I Math. 339 (2004) 667–672.
- A. Barret and G. Reddien, On the reduced basis method. Z. Angew. Math. Mech. 75 (1995) 543–549. [MathSciNet]
- T. Bui-Thanh, K. Willcox and O. Ghattas, Model reduction for large-scale systems with high-dimensional parametric input space. SIAM J. Sci. Comput. 30 (2008) 3270–3288. [CrossRef] [MathSciNet]
- Y. Chen, J.S. Hesthaven, Y. Maday and J. Rodríguez, A monotonic evaluation of lower bounds for Inf-Sup stability constants in the frame of reduced basis approximations. C. R. Acad. Sci. Paris Ser. I Math. 346 (2008) 1295–1300.
- 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]
- M.D. Gunzburger, Finite element methods for viscous incompressible flows. Academic Press (1989).
- J.S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Springer Texts in Applied Mathematics 54. Springer Verlag, New York (2008).
- D.B.P. Huynh, G. Rozza, S. Sen and A.T. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C. R. Acad. Sci. Paris Ser. I Math. 345 (2007) 473–478.
- L. Machiels, Y. Maday, I.B. Oliveira, A.T. Patera and D. Rovas, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. C. R. Acad. Sci. Paris Ser. I Math. 331 (2000) 153–158. [CrossRef] [MathSciNet]
- Y Maday, Reduced Basis Method for the Rapid and Reliable Solution of Partial Differential Equations, in Proceeding ICM Madrid (2006).
- Y. Maday, A.T. Patera and D.V. Rovas, A blackbox reduced-basis output bound method for noncoercive linear problems, in Nonlinear Partial Differential Equations and Their Applications, D. Cioranescu and J.L. Lions Eds., Collège de France Seminar XIV, Elsevier Science B.V. (2002) 533–569.
- D.A. Nagy, Modal representation of geometrically nonlinear behaviour by the finite element method. Comput. Struct. 10 (1979) 683–688. [CrossRef]
- N.C. Nguyen, K. Veroy and A.T. Patera. Certified real-time solution of parametrized partial differential equations, in Handbook of Materials Modeling, S. Yip Ed., Springer (2005) 1523–1558.
- A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA Journal 18 (1980) 455–462. [CrossRef]
- J.S. Peterson, The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10 (1989) 777–786. [CrossRef]
- C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A.T. Patera and G. Turinici, Reliable realtime solution of parametrized partial differential equations: Reduced-basis output bound methods. J. Fluids Engineering 124 (2002) 70–80. [CrossRef]
- 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: Application to transport and continuum mechanics. Arch. Comput. Methods Eng. 15 (2008) 229–275. [CrossRef] [MathSciNet]
- S. Sen, K. Veroy, D.B.P. Huynh, S. Deparis, N.C. Nguyen and A.T. Patera, “Natural norm” a posteriori error estimators for reduced basis approximations. J. Comput. Phys. 217 (2006) 37–62. [CrossRef] [MathSciNet]
Volume 43, Number 6, November-December 2009
|Page(s)||1099 - 1116|
|Published online||21 August 2009|