On the Convergence of Eigenvalues for Mixed Formulations

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volumn 25, Issue 1-2, 1997, Pages 131-154

  Boffi, Daniele ^a   Brezzi, Franco ^a   Gastaldi, Lucia ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000979322     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. BABUSKA, Error-Bounds for Finite Element Method, Numer. Math. 16 (1971), 322-333.
2. I . BABUSKA, On the finite element method with Lagrangian multipliers, Numer. Math. 20 (1973), 179-192.
3. I . BABUSKA - J . E . OsBORN, "Handbook of Numerical Analysis", vol. I I, ch. Eigenvalue Problems, North-Holland, 1991, pp. 641-788.
4. K . J . B A T H E - C . NiTiKiTPAiBœN - X . WANG , A mixed displacement-based finite element formulation/or acoustic fluid-structure interaction. Computers & Structures 56 (1995), 225¬ 237.
5. D . BoFFi - F . B R E Z Z I - L . GASTALDI, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form, submitted to Math. Comp., 1997.
6. J . M. BoLAND - R . NicoLAiDES, On the stability of bilinear-constant velocity-pressure finite elements, Numer. Math. 44 (1984), 219-222.
7. J . H . BRAMBLE - J . E . OSBORN, Rate of convergence for nonselfadjoint eigenvalue approximations. Math. Comp. 27 (1973), 525-549.
8. F. B R E Z Z I, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O. Anal. Numer. 8 (1974), 129-151.
9. F. BREZZI - M. FORTIN, "Mixed and Hybrid Finite Element Methods", Springer-Verlag, New York, 1991.
10. F . B R E Z Z I - J . DOUGLAS J R. - M. FORTIN - L . D. M A R I N I, Efficient rectangular mixed finite elements in two and three space variables, R. A. I. R. O. Model. Math. Anal. Numer. 21 (1987), 237-250.
11. F . B R E Z Z I - J . DOUGLAS J R. - L . D. M A R I N I, TWO families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), 217-235.
12. P. G . CIARLET, "The Finite Element Method for Elliptic Problems", North-Holland, Amsterdam, 1978.
13. P. G . CIARLET - P.-A. RAVIART, A mixed finite element method for the biharmonic equation, in "Mathematical Aspects of Finite Element in Partial Differential Equations", C. de Boor (ed.). Academic Press, New York, 1974, 125-143.
14. J . F A L K - J . E . OSBORN, Error estimates for mixed methods, R . A . I . R . O . Anal. Numer. 4 (1980), 249-277.
15. M . FORTIN, An analysis of the convergence of mixed finite element methods, R. A. I. R. O. Anal. Numer. 11 (1977), 341-354.
16. R . GLOWINSKI, Approximations externes par éléments finis de Lagrange d'ordre un et deux, du problème de Dirichlet pour l'opérateur biharmonique. Méthodes itératives de résolution des problèmes approchés, "Topics in Numerical Analysis", J. Miller (ed.). Academic Press, New York, 1973, 123-171.
17. P. GRISVARD, "Elliptic Problems in Non-Smooth Domains", Pitman, Marshfields, Mass., 1985.
18. C. JOHNSON - J . PITKÄRANTA, Analysis of some mixed finite element methods related to reduced integration. Math. Comp. 38 (1982), 375-400.
19. R . B . KELLOGG - J . E . OSBORN, A regularity result for the Stokes problem, J . Funct. Anal. 21(1976), 397-431.
20. B. MERCIER, Numerical solution of the biharmonic problem by mixed finite elements of class C^, Boll. U.M.1.10 (1974), 133-149.
21. B. MERCIER - J . E . OSBORN - J . RAH>AZ - P.-A. RAVI ART, Eigenvalue approximation by mixedandhybridmethods. Math. Comp. 36 (1981), 427-453.
22. J . T. ODEN - O . JACQUOTTE, Stability of some mixed finite element methods for Stokesian flows. Comp. Methods Appi. Mech. Eng. 43 (1984), 231-247.
23. J . E . OSBORN, Eigenvalue approximations by mixed methods, in "Advances in Computer Methods for Partial Differential Equations I I I ", R. Vichnevetsky and R. Stepleman (eds.), New Brunswick, 1979, 158-161.
24. P.-A. R A V I ART - J . M. THOMAS, A mixed finite element method for second order elliptic problems, in "Mathematical Aspects of the Finite Element Method", I. Galligani and E. Magenes (eds.), Lecture Notes in Math., Springer-Verlag, New York, 1977, 292-315.
25. R . SCHOLZ, A mixed methodfor fourth order problems using linearfinite elements, R. A. I. R. O. Anal. Numer. 12 (1978), 85-90.
26. X . WANG - K . J . BATHE, On mixed elements for acoustic fiuid-structure interaction, M^ AS, 7 (1997), 329-344.