A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations
Ohmori, Katsushi ; Ushijima, Teruo
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 18 (1984), p. 309-332 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1984__18_3_309_0,
     author = {Ohmori, Katsushi and Ushijima, Teruo},
     title = {A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {18},
     year = {1984},
     pages = {309-332},
     mrnumber = {751761},
     zbl = {0586.65080},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1984__18_3_309_0}
}

Ohmori, Katsushi; Ushijima, Teruo. A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 18 (1984) pp. 309-332. http://gdmltest.u-ga.fr/item/M2AN_1984__18_3_309_0/

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. | Numdam | MR 610595 | Zbl 0466.76090

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. | Numdam | MR 365287 | Zbl 0338.90047

3. P. G. Ciarlet, Discrete maximum principle for finite-difference operators, Aeq. Math., Vol. 4, 1970, pp. 338-352. | MR 292317 | Zbl 0198.14601

4. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978. | MR 520174 | Zbl 0383.65058

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. | MR 375802 | Zbl 0251.65069

6. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience Publishers, New York, 1962. | MR 65391 | Zbl 0099.29504

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. | Numdam | MR 343661 | Zbl 0302.65087

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. 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. | Zbl 0373.65047

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. | MR 684080 | Zbl 0468.76087

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. F. Kikuchi, Discrete maximum principle and artificial viscosity in finite element approximation to convective diffusion equations, ISAS Report., No. 550, 1977.

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. | MR 647391

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. | MR 542377 | Zbl 0459.65073

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. | MR 431752 | Zbl 0364.65082

16. R. Temam, Navier-Stokes Equations, North Holland, Amsterdam, 1977. | Zbl 0383.35057

17. F. Thomasset, Implementation of Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York, 1982. | MR 720192 | Zbl 0475.76036

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. | MR 754025 | Zbl 0663.76113