A finite element approximation of three dimensional motion of a Bingham fluid

Jong Uhn Kim

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 2, page 293-333
  • ISSN: 0764-583X

How to cite

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Kim, Jong Uhn. "A finite element approximation of three dimensional motion of a Bingham fluid." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.2 (1989): 293-333. <http://eudml.org/doc/193561>.

@article{Kim1989,
author = {Kim, Jong Uhn},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {initial-boundary value problem; Bingham fluid; backward Euler scheme; conforming piecewise linear finite elements; penalty method; convergence},
language = {eng},
number = {2},
pages = {293-333},
publisher = {Dunod},
title = {A finite element approximation of three dimensional motion of a Bingham fluid},
url = {http://eudml.org/doc/193561},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Kim, Jong Uhn
TI - A finite element approximation of three dimensional motion of a Bingham fluid
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 2
SP - 293
EP - 333
LA - eng
KW - initial-boundary value problem; Bingham fluid; backward Euler scheme; conforming piecewise linear finite elements; penalty method; convergence
UR - http://eudml.org/doc/193561
ER -

References

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  1. [1] D. BEGIS, Analyse numérique de l'écoulement d'un fluide de Bingham, Thèse Université de Paris, 1972. 
  2. [2] L. CATTABRIGA, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend Mat Sem. Univ. Padova, 31, 1961, p. 300-340. Zbl0116.18002MR138894
  3. [3] P. G. CIARLET, The Finite Element Method for Elhptic Problems, North-Holland, Amsterdam-New York-Oxford, 1978. Zbl0383.65058MR520174
  4. [4] G. DUVAUT, and J. L. LIONS, Écoulement d'un fluide rigide viscoplastiqueincompressible, C. R. Acad Sc. Paris, T 270, 1970, pp. 58-61. Zbl0194.57604MR261154
  5. [5] G. DUVAUT and J. L. LIONS, Inequalities in Mechanics and Physics, Springer-Verlag, Berlm-Heidelberg-New York, 1976. Zbl0331.35002MR521262
  6. [6] M. FORTIN, Calcul numérique des écoulements des fluides de Bingham et desfluides newtomens incompressibles par la méthode des éléments finis, Thèse, Université de Paris, 1972. 
  7. [7] D. GILBARG, and N. S. TRUDINGER, Elliptic Partial Differential Equations ofsecond order, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0361.35003MR473443
  8. [8] V. GiRAULT and P. A. RAVIART, Finite element Approximation of the Navier-Stokes Equations, Lecture Notes in Math. Vol. 749, Springer-Verlag, 1979. Zbl0413.65081MR548867
  9. [9] R. GLOWINSKI, Sur l'écoulement d'un fluide de Bmgham dans une conduite cylindrique, J. Mech. 13 (4), 1974, p 601-621. Zbl0324.76004MR371245
  10. [10] R. GLOWINSKI, Numencal Methods for Nonhnear vanational Problems, Springer-Verlag, New York-Berlin-Heidelberg, 1984. 
  11. [11] R. GLOWINSKI, J. L. LIONS, and R. TREMOLIERES, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam-New York-Oxford, 1981. Zbl0463.65046MR635927
  12. [12] J. G. HEYWOOD, and R. RANNACHER, Finite Element Approximation of the Nonstationary Navier-Stokes problem, Part II, SIAM J. Num. Anal., 23, No 4, 1986, p 750-777. Zbl0611.76036MR849281
  13. [13] J. KIM, On the initial-boundary value problem for a Bingham fluid in a threedimensional domain, Trans. Amer. Math. Soc., Vol. 304, No 2, 1987, p. 751-770. Zbl0635.35054MR911094
  14. [14] J. KIM, Semi-discretization Method for three dimensional motion of a Bingham fluid, preprint. Zbl0706.35113
  15. [15] J. L. LIONS, Quelques Methodes de Resolution des Problèmes aux Limites Non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  16. [16] R. TEMAM, Une Methode d'Approximation de la Solution des Equations deNavier-Stokes, Bull. Soc. Math. France, Vol. 96, 1968, p. 115-152. Zbl0181.18903MR237972
  17. [17] R. TEMAN, Navier-Stokes Equations, North-Holland, Amsterdam-New York-Oxford, 1984. Zbl0568.35002MR769654
  18. [18] R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia, 1983. Zbl0833.35110MR764933
  19. [19] H. TRIEBEL, Interpolation Theory,Function spaces, Differential Operators, North-Holland, Amsterdam-New-Oxford, 1978. Zbl0387.46032MR503903

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