Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 2, 2000, Pages 153-158

  Machiels, Luc ^a   Maday, Yvon ^b,c   Oliveira, Ivan B ^a   Patera, Anthony T ^a   Rovas, Dimitrios V ^a  

^a USA   (United States)

^b Lab Applic Sci du Calcul Intensif   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034660787     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)00270-6     Document Type: Article

References (7)

1. [1] Babuška I., Osborn J., Eigenvalue problems, in: Handbook of Numerical Analysis, Vol. II, Ciarlet P.G., Lions J.-L. (Eds.), Elsevier, 1991, pp. 641-787.
2. [2] Fink J.P., Rheinboldt W.C., On the error behavior of the reduced basis technique for nonlinear finite element approximations, ZAMM 63 (1983) 21-28.
3. [3] Machiels L., Maday Y., Patera A.T., Output bounds for reduced-order approximations of elliptic partial differential equations, Comput. Meth. Appl. Mech. Engrg., (to appear).
4. [4] Maday Y., Patera A.T., Peraire J., A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem, C. R. Acad. Sci. Paris, Série I 327 (1998) 823-828.
5. [5] Noor A.K., Peters J.M., Reduced basis technique for nonlinear analysis of structures, AIAA J. 18 (1980) 455-462.
6. [6] Paraschivoiu M., Peraire J., Maday Y., Patera A.T., Fast bounds for outputs of partial differential equations, in: Computational Methods for Optimal Design and Control, Borggaard J., Burns J., Cliff E., Schreck S. (Eds.), Birkhäuser, 1998, pp. 323-360.
7. [7] Porsching T.A., Estimation of the error in reduced basis method solution of nonlinear equations, Math. Comput. 45 (172) (1985) 487-496.