Volume 40, Number 3, May-June 2006
|Page(s)||529 - 552|
|Published online||22 July 2006|
- R. Aris, Vectors, tensors and the basic equations of fluid mechanics. Dover Publications (1989).
- I. Babuska, Error-bounds for finite element method. Numer. Math. 16 (1971) 322–333. [CrossRef] [MathSciNet]
- B.F. Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. [CrossRef] [MathSciNet]
- B.F. Belgacem, C. Bernardi, N. Chorfi and Y. Maday, Inf-sup conditions for the mortar spectral element discretization of the Stokes problem. Numer. Math. 85 (2000) 257–281. [CrossRef] [MathSciNet]
- C. Bernardi and Y. Maday, Polynomial approximation of some singular functions. Appl. Anal. 42 (1992) 1–32. [CrossRef] [MathSciNet]
- F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal. Numér. 8 (1974) 129–151.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag (1991).
- J.P. Fink and W.C. Rheinboldt, On the error behavior of the reduced basis technique in nonlinear finite element approximations. Z. Angew. Math. Mech. 63 (1983) 21–28. [CrossRef] [MathSciNet]
- W.J. Gordon and C.A. Hall, Construction of curvilinear co-ordinate systems and applications to mesh generation. Int. J. Numer. Meth. Eng. 7 (1973) 461–477. [CrossRef]
- Y. Maday and A.T. Patera, Spectral element methods for the Navier-Stokes equations. In Noor A. Ed., State of the Art Surveys in Computational Mechanics (1989) 71–143.
- Y. Maday and E.M. Rønquist, A reduced-basis element method. J. Sci. Comput. 17 (2002) 447–459. [CrossRef] [MathSciNet]
- Y. Maday and E.M. Rønquist, The reduced-basis element method: application to a thermal fin problem. SIAM J. Sci. Comput. 26 (2004) 240–258. [CrossRef] [MathSciNet]
- Y. Maday, A.T. Patera, and E.M. Rønquist, The PN x PN-2 method for the approximation of the Stokes problem. Technical Report No. 92009, Department of Mechanical Engineering, Massachusetts Institute of Technology (1992).
- Y. Maday, D. Meiron, A.T. Patera and E.M. Rønquist, Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. SIAM J. Sci. Stat. Comp. (1993) 310–337.
- A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA J. 19 (1980) 455–462. [CrossRef]
- C. Prud'homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera and G. Turinici, Reliable real-time solution of parametrized partial differential equations: Reduced basis output bound methods. J. Fluid Eng. 124 (2002) 70–80. [CrossRef]
- P.A. Raviart and J.M. Thomas, A mixed finite element method for 2-nd order elliptic problems, in Mathematical Aspects of Finite Element Methodes, Lec. Notes Math. 606 I. Galligani and E. Magenes Eds., Springer-Verlag (1977).
- D.V. Rovas, Reduced-Basis Output Bound Methods for Parametrized Partial Differential Equations. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (October 2002).
- K. Veroy, C. Prud'homme, D.V. Rovas and A.T. Patera, A Posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations (AIAA Paper 2003-3847), in Proceedings of the 16th AIAA Computational Fluid Dynamics Conference (June 2003).
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