Free access
Issue
ESAIM: M2AN
Volume 40, Number 3, May-June 2006
Page(s) 529 - 552
DOI http://dx.doi.org/10.1051/m2an:2006021
Published online 22 July 2006
  1. R. Aris, Vectors, tensors and the basic equations of fluid mechanics. Dover Publications (1989).
  2. I. Babuska, Error-bounds for finite element method. Numer. Math. 16 (1971) 322–333. [CrossRef] [MathSciNet]
  3. B.F. Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. [CrossRef] [MathSciNet]
  4. 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]
  5. C. Bernardi and Y. Maday, Polynomial approximation of some singular functions. Appl. Anal. 42 (1992) 1–32. [CrossRef] [MathSciNet]
  6. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal. Numér. 8 (1974) 129–151.
  7. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag (1991).
  8. 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]
  9. 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]
  10. 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.
  11. Y. Maday and E.M. Rønquist, A reduced-basis element method. J. Sci. Comput. 17 (2002) 447–459. [CrossRef] [MathSciNet]
  12. 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]
  13. 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).
  14. 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.
  15. A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA J. 19 (1980) 455–462. [CrossRef]
  16. 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]
  17. 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).
  18. D.V. Rovas, Reduced-Basis Output Bound Methods for Parametrized Partial Differential Equations. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (October 2002).
  19. 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).

Recommended for you