On the convergence of eigenvalues for mixed formulations

 Access to full text

 Full (PDF)

1. [1] I BabuŠka, Error-Bounds for Finite Element Method, Numer. Math.16 (1971), 322-333. Zbl0214.42001MR288971
2. [2] I Babuška, On the finite element method with Lagrangian multipliers, Numer. Math.20 (1973), 179-192. Zbl0258.65108MR359352
3. [3] I Babuška - J.E. Osborn, "Handbook of Numerical Analysis", vol. II, ch. Eigenvalue Problems, North-Holland, 1991, pp. 641-788. Zbl0875.65087MR1115240
4. [4] K.J. Bathe - C. Nitikitpaiboon - X. Wang, A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers &Structures56 (1995), 225-237. Zbl1002.76536MR1336298
5. [5] D. Boffi - F. Brezzi - L. Gastaldi, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form, submitted to Math. Comp., 1997. Zbl0938.65126MR1642801
6. [6] J.M. Boland - R. Nicolaides, On the stability of bilinear-constant velocity-pressure finite elements, Numer. Math.44 (1984), 219-222. Zbl0544.76030MR753954
7. [7] J.H. Bramble - J.E. Osborn, Rate of convergence for nonselfadjoint eigenvalue approximations, Math. Comp.27 (1973), 525-549. Zbl0305.65064MR366029
8. [8] F. Brezzi, 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. Zbl0338.90047MR365287
9. [9] F. Brezzi - M. Fortin, "Mixed and Hybrid Finite Element Methods", Springer-Verlag, New York, 1991. Zbl0788.73002MR1115205
10. [10] F. Brezzi - J. DouglasJr. - M. Fortin - L.D. Marini, Efficient rectangular mixed finite elements in two and three space variables, R.A.I.R.O. Model. Math. Anal. Numer.21 (1987), 237-250. Zbl0689.65065MR921828
11. [11] F. Brezzi - J. DouglasJr. - L.D. Marini, Two families of mixed finite elements for second order elliptic problems, Numer. Math.47 (1985), 217-235. Zbl0599.65072MR799685
12. [12] P.G. Ciarlet, "The Finite Element Method for Elliptic Problems ", North-Holland, Amsterdam, 1978. Zbl0383.65058MR520174
13. [13] P.G. Ciarlet - P.-A. Raviart, A mixed finite element methodfor the biharmonic equation, in "Mathematical Aspects of Finite Element in Partial Differential Equations", C. de Boor (ed.), Academic Press, New York, 1974, 125-143. Zbl0337.65058MR657977
14. [14] J. Falk - J.E. Osborn, Error estimates for mixed methods, R.A.I.R.O. Anal. Numer.4 (1980), 249-277. Zbl0467.65062MR592753
15. [15] M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O. Anal. Numer.11 (1977), 341-354. Zbl0373.65055MR464543
16. [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. Zbl0277.35003MR351120
17. [17] P. Grisvard, "Elliptic Problems in Non-Smooth Domains", Pitman, Marshfields, Mass., 1985. Zbl0695.35060
18. [18] C. Johnson - J. Pitkäranta, Analysis of some mixed finite element methods related to reduced integration, Math. Comp.38 (1982), 375-400. Zbl0482.65058MR645657
19. [19] R.B. Kellogg - J.E. Osborn, A regularity result for the Stokes problem, J. Funct. Anal.21 (1976), 397-431. Zbl0317.35037MR404849
20. [20] B. Mercier, Numerical solution of the biharmonic problem by mixed finite elements of class C°, Boll. U.M.I.10 (1974), 133-149. Zbl0332.65058MR378442
21. [21] B. Mercier - J.E. Osborn - J. Rappaz - P.-A. Raviart, Eigenvalue approximation by mixed and hybrid methods, Math. Comp.36 (1981), 427-453. Zbl0472.65080MR606505
22. [22] J.T. Oden - O. Jacquotte, Stability of some mixed finite element methods for Stokesian flows, Comp. Methods Appl. Mech. Eng.43 (1984), 231-247. Zbl0598.76033MR745509
23. [23] J.E. Osborn, Eigenvalue approximations by mixed methods, in "Advances in Computer Methods for Partial Differential Equations III", R. Vichnevetsky and R. Stepleman (eds.), New Brunswick, 1979, 158-161. MR603467
24. [24] P.-A. Raviart - 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. Zbl0362.65089MR483555
25. [25] R. Scholz, A mixed method for fourth order problems using linear finite elements, R.A.I.R.O. Anal. Numer.12 (1978), 85-90. Zbl0382.65059MR483557
26. [26] X. Wang - K.J. Bathe, On mixed elements for acoustic fluid-structure interaction, M3AS, 7 (1997), 329-344. Zbl0881.76053MR1443789

1. Qun Lin, Hehu Xie, A Superconvergence result for mixed finite element approximations of the eigenvalue problem
2. Evgenii V. Chizhonkov, Maxim A. Olshanskii, On the domain geometry dependence of the LBB condition
3. Evgenii V. Chizhonkov, Maxim A. Olshanskii, On the domain geometry dependence of the LBB condition
4. Francesca Gardini, Mixed approximation of eigenvalue problems: A superconvergence result
5. Qun Lin, Hehu Xie, A Superconvergence result for mixed finite element approximations of the eigenvalue problem
6. Patrick Ciarlet Jr., François Lefèvre, Stéphanie Lohrengel, Serge Nicaise, Weighted regularization for composite materials in electromagnetism
7. Wei Chen, Qun Lin, Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method