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Error estimates for some mixed finite element methods for parabolic type problems. (English) Zbl 0476.65074

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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References:
[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. Zbl0093.10401 MR125307 · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[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. Zbl0378.65061 MR448947 · Zbl 0378.65061 · doi:10.2307/2006116
[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. Zbl0305.65064 MR366029 · Zbl 0305.65064 · doi:10.2307/2005658
[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. Zbl0364.65084 MR448926 · Zbl 0364.65084 · doi:10.1137/0714015
[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. Zbl0306.65073 MR388805 · Zbl 0306.65073 · doi:10.1007/BF02417101
[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. Zbl0338.90047 MR365287 · Zbl 0338.90047 · eudml:193255
[7] 7. A. CALDERON and A. ZYGMUND, On theExistence of Certain Singuiar Integrals, Acta Math., Vol.88, 1952, pp. 85-139. Zbl0047.10201 MR52553 · Zbl 0047.10201 · doi:10.1007/BF02392130
[8] 8. G. DUVAUT and J. L. LIONS, Les inéquations en mécanique et enphysique, Dunod, Paris, 1972. Zbl0298.73001 MR464857 · Zbl 0298.73001
[9] 9. R. FALK and J. OSBORN, Error Estimates for Mixed Methods, Technical report, The Mathematics Research Center, University of Wisconsin-Madison, 1979. Zbl0121.24305 MR592753 · Zbl 0121.24305
[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. Zbl0399.76035 MR519017 · Zbl 0399.76035 · eudml:193328
[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. Zbl0427.73072 MR483904 · Zbl 0427.73072 · doi:10.1007/BF01403910 · eudml:132541
[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 · Zbl 0362.65089
[14] 14. R. SCHOLZ, L \infty -Convergence of Saddle-Point Approximation for Second Order Problems,R.A.I.R.O., Anal. Numér., Zbl0356.35026 · Zbl 0356.35026 · eudml:193297
[15] 15. R. TEMAM, Navier-Stokes’ Equations, North Holland. Amsterdam, 1977. Zbl0383.35057 · Zbl 0383.35057
[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. Zbl0419.65073 MR514809 · Zbl 0419.65073 · doi:10.2307/2006026
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