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

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
35K20Second order parabolic equations, initial boundary value problems
Full Text: EuDML
[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