On a conservation upwind finite element scheme for convective diffusion equations

Kinji Baba; Masahisa Tabata

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 1, page 3-25
  • ISSN: 0764-583X

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Baba, Kinji, and Tabata, Masahisa. "On a conservation upwind finite element scheme for convective diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.1 (1981): 3-25. <http://eudml.org/doc/193369>.

@article{Baba1981,
author = {Baba, Kinji, Tabata, Masahisa},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {conservative upwind scheme; convective diffusion equations; discrete maximum principle},
language = {eng},
number = {1},
pages = {3-25},
publisher = {Dunod},
title = {On a conservation upwind finite element scheme for convective diffusion equations},
url = {http://eudml.org/doc/193369},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Baba, Kinji
AU - Tabata, Masahisa
TI - On a conservation upwind finite element scheme for convective diffusion equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 1
SP - 3
EP - 25
LA - eng
KW - conservative upwind scheme; convective diffusion equations; discrete maximum principle
UR - http://eudml.org/doc/193369
ER -

References

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  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. Zbl0386.76067
  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. Zbl0214.41405MR290524
  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. Zbl0243.41004MR336957
  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. Zbl0251.65069MR375802
  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. Zbl0373.65047
  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. Zbl0466.76086
  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. Zbl0353.65065
  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. Zbl0436.76062
  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. Zbl0468.76087
  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. Zbl0358.65102MR448957
  13. 13. M. TABATA, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18 (1978), 327-351. Zbl0391.65038MR495024
  14. 14. M. TABATA, L -analysis of the finite element method, Lecture Notes in Num. Appl. Anal, 1 (1979) 25-62, Kinokuniya, Tokyo. Zbl0458.65096MR690436
  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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