Approximation of the three-field Stokes system via optimized quadrilateral finite elements

V. Ruas; J. H. Carneiro de Araújo; M. A. M. Silva Ramos

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 1, page 107-127
  • ISSN: 0764-583X

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Ruas, V., Carneiro de Araújo, J. H., and Silva Ramos, M. A. M.. "Approximation of the three-field Stokes system via optimized quadrilateral finite elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.1 (1993): 107-127. <http://eudml.org/doc/193691>.

@article{Ruas1993,
author = {Ruas, V., Carneiro de Araújo, J. H., Silva Ramos, M. A. M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {bubble tensors; number of degrees of freedom; linear problem},
language = {eng},
number = {1},
pages = {107-127},
publisher = {Dunod},
title = {Approximation of the three-field Stokes system via optimized quadrilateral finite elements},
url = {http://eudml.org/doc/193691},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Ruas, V.
AU - Carneiro de Araújo, J. H.
AU - Silva Ramos, M. A. M.
TI - Approximation of the three-field Stokes system via optimized quadrilateral finite elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 1
SP - 107
EP - 127
LA - eng
KW - bubble tensors; number of degrees of freedom; linear problem
UR - http://eudml.org/doc/193691
ER -

References

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  1. [1] R. A. ADAMS, Sobolev Spaces, Academic Press N. Y., 1968. Zbl1098.46001MR450957
  2. [2] R. B. BlRD, R. C. ARMSTRONG and O. HASSAGER, Dynamics of polymeric liquids, Vol 1, Fluid Mechanics, Second Edition, John Wiley & Sons, N. Y., 1987. 
  3. [3] J. BARANGER and D. SANDRI, Approximation par element finis d'écoulements de fluides viscoélastiques Existence de solutions approchées et majorations d'erreur I Contraintes continues, C. R. Acad. Sci. Paris, Tome 312, Série I (1991), 541-544. Zbl0718.76010MR1099689
  4. [4] M. BERCOVIER and O. PIRONNEAU, Error estimates for the finite element method solution of the Stokes problem in the primitive variables, Numer. Math., 33 (1979), 211-224. Zbl0423.65058MR549450
  5. [5] J. H. CARNEIRO DE ARAÚJO, Métodos de Elementos Finitos Otimizados para o Sistema de Stokes Associado a Problemas de Viscoelasticidade, Doctoral dissertation, Pontificia Universidade Católica do Rio de Janeiro, 1991. 
  6. [6] M. S. ENGELMAN, R. L. SANI, P. M. GRESHO and M. BERCOVIER, Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements, Int. J. Num. Methods in Fluids, 2 (1982), 25-42. Zbl0483.76013MR643172
  7. [7] M. FORTIN and A. FORTIN, A new approach for the FEM simulation of viscoelastic flows, J. Non-Newtonian Fluid Mech., 32 (1989) 295-310. Zbl0672.76010
  8. [8] M. FORTIN and R. PIERRE, On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows, Comput. Methods Appl. Mech, Engrg, 73 (1989) 341-350. Zbl0692.76002MR1016647
  9. [9] J. M. MARCHAL and M. CROCHET, A new mixed finite element for calculating viscoelastic flow, J. Non-Newtonian Fluid Mech., 26 (1987) 77-117. Zbl0637.76009
  10. [10] V. RUAS, An optimal three-field finite element approximation of the Stokes system with continuous extra stresses (to appear). Zbl0797.76045MR1266524
  11. [11] V. RUAS, A convergent three-field quadrilatéral finite element method for simulating viscoelastic flow on irregular meshes. Revue Européenne des Eléments Finis, Vol. 1, 4 (1992), 391-406. Zbl0924.76060MR1266524
  12. [12] V. RUAS and J. H. CARNEIRO DE ARAÚJO, Un método mejorado de segundo orden para la simulación de flujo viscoelástico con elementos finitos quadrilaterales, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 8, 1 (1992), 77-85. MR1160319

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