A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations

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1. 1. K. BABA and M. TABATA, On a conservative upwind finite element scheme for convective diffusion equations, R.A.I.R.O., Anal. Numér., Vol. 15, 1981, pp. 3-25. Zbl0466.76090MR610595
2. 2. F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O., Anal. Numér., Vol. 8, 1974, pp. 129-151. Zbl0338.90047MR365287
3. 3. P. G. CIARLET, Discrete maximum principle for finite-difference operators, Aeq. Math., Vol. 4, 1970, pp. 338-352. Zbl0198.14601MR292317
4. 4. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978. Zbl0383.65058MR520174
5. 5. P. G. CIARLET and P.-A. RAVIART, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg., Vol. 2, 1973, pp. 17-31. Zbl0251.65069MR375802
6. 6. R. COURANT and D. HILBERT, Methods of Mathematical Physics, Vol. II, Interscience Publishers, New York, 1962. Zbl0099.29504MR65391
7. 7. M. CROUZEIX and P.-A. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, R.A.I.R.O., Anal. Numér., Vol. 7, 1973, pp. 33-76. Zbl0302.65087MR343661
8. 8. A. DERVIEUX and F. THOMASSET, Sur l'approximation d'écoulements multifluides incompressibles visqueux par des éléments finis triangulaires de degré un, Rapports de Recherche 67 (LABOLIA INRIA), Avril, 1981. 
9. 9. H. FUJII, Some remarks on finite element analysis of time-dependent field problem, Theory and Practice in Finite Element Structural Analysis, Y. Yamada and R. H. Gallagher, Eds., University of Tokyo Press, 1973, pp. 91-106. Zbl0373.65047
10. 10. T. IKEDA, Artificial viscosity in finite element approximations to the diffusion equations with drift terms, H. Fujita and M. Yamaguti, Eds., Lecture Notes in Num. Appl. Anal., Kinokuniya, Tokyo, Vol. 2, 1980, pp. 59-78. Zbl0468.76087MR684080
11. 11. H. KANAYAMA, Discrete models for salinity distribution in a bay - Conservative law and maximum principle, Proc. Japan Nat. Congr. for Applied Mech., 1980, Theoretical and Applied Mechanics, Vol. 28, 1980, pp. 559-579. 
12. 12. F. KIKUCHI, Discrete maximum principle and artificial viscosity in finite element approximation to convective diffusion equations, ISAS Report., No. 550, 1977. 
13. 13. F. KIKUCHI and T. USHIJIMA, Theoretical analysis of some finite element schemes for convective diffusion equations, R. H. Gallagher, D. H. Norrie, J. T. Oden and O. C. Zienkiewicz, Eds., Finite Elements in Fluids, John Wiley & Sons Ltd, Vol. 4, 1982, pp. 67-87. MR647391
14. 14. K. OHMORI, The discrete maximum principle for nonconforming finite element approximations to stationary convective diffusion equations, Math. Rep. Toyama Univ., Vol. 2, 1979, pp. 33-52. Corrections, ibid.,Vol. 4, 1981, pp. 179-182. Zbl0459.65073MR542377
15. 15. P.-A. RAVIART and J. M. THOMAS, Primal hybrid finite element methods for 2nd order elliptic equations, Math. Comp., Vol. 31, 1977, pp. 391-413. Zbl0364.65082MR431752
16. 16. R. TEMAM, Navier-Stokes Equations, North Holland, Amsterdam, 1977. Zbl0383.35057
17. 17. F. THOMASSET, Implementation of Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York, 1982. Zbl0475.76036MR720192
18. 18. T. USHIJIMA, On a certain finite element method of the upstream type applied to convective diffusion problems, China-France Symposium on the Finite Element Method, 1982. Zbl0663.76113MR754025

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