Error estimates for some mixed finite element methods for parabolic type problems

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1. 1. S. AGMON, A. DOUGLIS and L. NIRENBERG, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions, Comm. Pure AppL Math., Vol. 12, 1959, pp. 623-727. Zbl0093.10401MR125307
2. 2. G. A. BAKER, J. H. BRAMBLE and V. THOMÉE, Single Step Galerkin Approximations for Parabolic Problems, Math. Comp., Vol.31, 1977 pp. 818-847. Zbl0378.65061MR448947
3. 3. J. H. BRAMBLE and J. OSBORN, Rate of Convergence Estimates for Non-Selfadjoint Eigenvalue Approximations, Math. Comp., Vol. 27, 1973, pp. 525-549. Zbl0305.65064MR366029
4. 4. J. H. BRAMBLE, A. H. SCHATZ, V. THOMÉE and L. B. WAHLBIN, Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations, S.I.A.M. J. Numer. Anal., Vol. 14, 1977, pp. 218-241. Zbl0364.65084MR448926
5. 5. J. H. BRAMBLE and V. THOMÉE, Discrete Time Galerkin Methods for a Parabolic Boundary Value Problem, Annali di Matematica pura ed applicata, Vol. 101, 1974 pp. 115-152. Zbl0306.65073MR388805
6. 6. F. BREZZI, On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers, R.A.I.R.O., Anal. Numér., Vol.2, 1974, pp. 129-151. Zbl0338.90047MR365287
7. 7. A. CALDERON and A. ZYGMUND, On theExistence of Certain Singuiar Integrals, Acta Math., Vol.88, 1952, pp. 85-139. Zbl0047.10201MR52553
8. 8. G. DUVAUT and J. L. LIONS, Les inéquations en mécanique et enphysique, Dunod, Paris, 1972. Zbl0298.73001MR464857
9. 9. R. FALK and J. OSBORN, Error Estimates for Mixed Methods, Technical report, The Mathematics Research Center, University of Wisconsin-Madison, 1979. Zbl0467.65062MR592753
10. 10. C. JENSEN, A Mixed Finite Element Method with Curved Eléments, Technical report, Department of Computer Science, Chalmers University of Technology, 1979. 
11. 11. C. JOHNSON, A Mixed Finite Element Method for Navier-Stokes' Equatiom, R.A I. R.O., Anal. Numér., Vol. 12, 1978, pp. 335-348. Zbl0399.76035MR519017
12. 12. C. JOHNSON and B. MERCIER, Some Equilibrium Finite Element Methods for Two-Dimensional Elasticity Problems, Numer. Math., Vol. 30, 1978, pp. 103-116. Zbl0427.73072MR483904
13. 13. P. A. RAVIART and J. M. THOMAS, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Proc. of the Symposium on the Mathematîcal Aspects of the Finite Element Method, Rome, December, 1975. Zbl0362.65089
14. 14. R. SCHOLZ, $L_{\infty }$-Convergence of Saddle-Point Approximation for Second Order Problems,R.A.I.R.O., Anal. Numér., Zbl0356.35026
15. 15. R. TEMAM, Navier-Stokes' Equations, North Holland. Amsterdam, 1977. Zbl0383.35057
16. 16. J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thèse, Université Pierre-et-Marie-Curie, Paris, 1977. 
17. 17. V. THOMÉE, Some Interior Estimates for Semidiscrete Galerkin Approximations for Parabolic Equations, Math. Comp., Vol.33, 1979, pp. 37-62. Zbl0419.65073MR514809

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