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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:

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[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
[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
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[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
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[8] 8. G. DUVAUT and J. L. LIONS, Les inéquations en mécanique et enphysique, Dunod, Paris, 1972. Zbl0298.73001 MR464857 · Zbl 0298.73001
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[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
[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
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