Rate of convergence estimates for the spectral approximation of a generalized eigenvalue problem

Numerische Mathematik

Volumn 79, Issue 3, 1998, Pages 349-369

  Conca, Carlos ^a   Durán, Mario ^b,c   Rappaz, Jacques ^d  

^a DEPARTAMENTO DE FÍSICA   (Chile)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^c CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^d EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041171354     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050343     Document Type: Article

References (19)

1. Aziz, A., Babuška, I. (1973): The mathematical foundations of the finite element method with applications to partial differential equations. Survey lectures on the mathematical foundations of the finite element method. Academic Press, New-York
2. Babuška, I. (1971): Error bounds for unite element methods. Numer. Math. 16, pp. 322-333
3. Babuška, I., Osborn, J.-E. (1991): Eigenvalue problems. Handbook of numerical analysis II. Finite element methods (part 1). North-Holland, Amsterdam
4. Brezzi, F. (1974): On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers. RAIRO Rech. Opér. 8, pp. 129-151
5. Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer-Verlag, Berlin
6. Ciarlet, PH. (1979): The finite element method for elliptic problems. North-Holland, Amsterdam
7. Conca, C., Durán, M. (1995): A numerical study of a spectral problem in solid-fluid type structures. Numer. Methods Partial Differential Equations 11, pp. 423-444
8. Conca, C., Durán, M., Planchard, J. (1992): A quadratic eigenvalue problem involving Stokes equations. Comput. Methods Appl. Mech. Engrg. 100, pp. 295-313
9. Conca, C., Durán, M., Planchard, J. (1992): A bound for the number of nonreal solutions of a quadratic eigenvalue problem. Adv. Math. Sci. Appl. 1, pp. 229-249
10. Fix, G. (1973): Eigenvalue approximation by the finite element method. Adv. Math. 10, pp. 300-316
11. Girault, V., Raviart, P.-A. (1986): Finite element methods for Navier-Stokes equations. Springer-Verlag, Berlin
12. Grisvard, P. (1992): Singularities in boundary value problems. Masson, Paris and Springer-Verlag, Berlin
13. Kato, T. (1976): Perturbation theory for linear operators. Springer-Verlag, Berlin
14. Kolata, W.G. (1978): Approximation of variationally posed eigenvalue problems. Numer. Math. 29, pp. 159-171
15. Mercier, B., Osborn, J.-E., Rappaz, J., Raviart, P.-A. (1981): Eigenvalue approximation by mixed and hybrid methods. Math. Comp. 36, pp. 427-453
16. Nečas, J. (1967): Les méthodes directes en théorie des équations elliptiques. Masson, Paris
17. Planchard, J. (1980): Computation of the acoustic eigenfrequencies of cavities containing a tube bundle. Comput. Methods Appl. Mech. Engrg. 24, pp. 125-135
18. Raviart, P.-A., Thomas, J.-M. (1983): Introduction à l'analyse numérique des équations aux dérivées partielles. Masson, Paris
19. Scott, R. (1979): Applications of Banach space interpolation to finite element theory. Functional analysis methods in numerical analysis. Lecture notes in Mathematics 701, pp. 298-318, Springer-Verlag, Berlin