Free Access
Issue
RAIRO. Anal. numér.
Volume 15, Number 1, 1981
Page(s) 3 - 25
DOI https://doi.org/10.1051/m2an/1981150100031
Published online 31 January 2017
  1. 1. K. BABA and S. YOSHII, An upwind scheme for convective diffusion equation by finite element method, Proceedings of VIIIth International Congress on Application of Mathematics in Engineering, Weimar/DDR, 1978. [Zbl: 0386.76067]
  2. 2. J. H. BRAMBLE and S. R. HILBERT, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math., 16 (1971), 362-369. [EuDML: 132041] [MR: 290524] [Zbl: 0214.41405]
  3. 3. P. G. CIARLET and P. A. RAVIART, General Lagrange and Hermite interpolationin Rn with applications to finite element methods, Arch. Rational Mech. AnaL,46 (1971), 177-199. [MR: 336957] [Zbl: 0243.41004]
  4. 4. P. G. CIARLET and P. A. RAVIART, Maximum principle and uniform convergence for the finite element method, Computer Methods in Applied Mechanics and Engineering, 2 (1973), 17-31. [MR: 375802] [Zbl: 0251.65069]
  5. 5. H. FUJII, Some remarks on finite element analysis of time-dependent field problems,Theory and practice in finite element structural analysis, ed. by Yamada, Y. and Gallagher, R. H., 91-106, Univ. of Tokyo Press, Tokyo, 1973. [Zbl: 0373.65047]
  6. 6. R. GORENFLO, Energy conserving discretizations of diffusion equations, Paper submitted for publication in the Proceedings of the Conference on Numerical Methods in Keszthely/Hungary, 1977. [Zbl: 0466.76086]
  7. 7. F. C. HEINRICH, P. S. HUYAKORN, O. C. ZIENKIEWICZ and A. R. MITCHELL, An " upwind "finite element scheme for two dimensional convective-transport equation,Int. J. Num. Meth. Engng., 11 (1977), 131-143. [Zbl: 0353.65065]
  8. 8. F. C. HEINRICH and O. C. ZIENKIEWICZ, The finite element method and " upwinding " techniques in the numerical solution of confection dominated flow problems, Preprint for the ASME winter annual meeting on fini te element methods for convection dominated flows, 1979. [Zbl: 0436.76062]
  9. 9. T. IKEDA, Artificial viscosity infinite element approximations to the diffusion equation with drift terms, to appear in Lecture Notes in Num. Appl. Anal., 2. [Zbl: 0468.76087]
  10. 10. H. KANAYAMA, Discrete models for salinity distribution in a bay-Conservation law and maximum principle, to appear in Theoretical and Applied Mechanics, 28.
  11. 11. F. KIKUCHI, The discrete maximum principle and artificial viscosity in finite element approximations to convective diffusion equations, Institute of Space and Aeronautical Science, University of Tokyo, Report n° 550 (1977).
  12. 12. M. TABATA, A finite element approximation corresponding to the upwind finite differencing, Memoirs of Numerical Mathematics, 4 (1977), 47-63. [MR: 448957] [Zbl: 0358.65102]
  13. 13. M. TABATA, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18 (1978), 327-351. [MR: 495024] [Zbl: 0391.65038]
  14. 14. M. TABATA, $L^\infty $-analysis of the finite element method, Lecture Notes in Num. Appl. Anal, 1 (1979) 25-62, Kinokuniya, Tokyo. [MR: 690436] [Zbl: 0458.65096]
  15. 15. M. TABATA, Some applications of the upwind finite element method, Theoretical and Applied Mechanics, 27 (1979), 277-282, Univ. of Tokyo Press, Tokyo.

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