Error estimates for a mixed finite element approximation of the Stokes equations

R. Verfürth

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1984)

  • Volume: 18, Issue: 2, page 175-182
  • ISSN: 0764-583X

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Verfürth, R.. "Error estimates for a mixed finite element approximation of the Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 18.2 (1984): 175-182. <http://eudml.org/doc/193431>.

@article{Verfürth1984,
author = {Verfürth, R.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element method; polygonal domain; discrete inf-sup condition; abstract error analysis},
language = {eng},
number = {2},
pages = {175-182},
publisher = {Dunod},
title = {Error estimates for a mixed finite element approximation of the Stokes equations},
url = {http://eudml.org/doc/193431},
volume = {18},
year = {1984},
}

TY - JOUR
AU - Verfürth, R.
TI - Error estimates for a mixed finite element approximation of the Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1984
PB - Dunod
VL - 18
IS - 2
SP - 175
EP - 182
LA - eng
KW - mixed finite element method; polygonal domain; discrete inf-sup condition; abstract error analysis
UR - http://eudml.org/doc/193431
ER -

References

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  1. 1 I BABUSKA, The finite element method with Lagrangian multipliers, Numer Math 20, pp 179-192, 1973 Zbl0258.65108MR359352
  2. 2 M BERCOVIER, O PIRONNEAU, Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numer Math 33, pp 211-224, 1979 Zbl0423.65058MR549450
  3. 3 C BERNARDI, G RAUGEL, Méthodes d'éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone non convexe, Calcolo 18, pp 255-291, 1981 Zbl0475.76035MR647827
  4. 4 F BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Anal Numér 8 (R-2), pp 129-151, 1974 Zbl0338.90047MR365287
  5. 5 Ph G CIARLET, The finite element method for elliptic problems, North Holland Publishing Company, 1978 Zbl0383.65058MR520174
  6. 6 Ph CLÉMENT, Approximation by finite element functions using local regulanzation, RAIRO Anal Numér 9 (R-2), pp 77-84, 1975 Zbl0368.65008MR400739
  7. 7 M CROUZIEUX, P -A RAVIART, Conforming and nonconforming fimte element methods for solving the stationary Stokes equations, RAIRO Anal Numér 7 (R-3), pp 33-76, 1973 Zbl0302.65087MR343661
  8. 8 V GIRAULT, P -A RAVIART, An analysis of a mixed finite element method for the Navier-Stokes équations, Numer Math 33, pp 235-271, 1979 Zbl0396.65070MR553589
  9. 9 V GIRAULT, P -A RAVIART, Finite element approximation of the Navier-Stokes equations, Springer Verlag, 1979 Zbl0413.65081MR548867
  10. 10 R GLOWINSKI, O PIRONNEAU, On a mixed finite element approximation of the Stokes problem I Convergence of the approximate solutions, Numer Math 33, pp 397-424, 1979 Zbl0423.65059MR553350
  11. 11 R B KELLOGG, J E OSBORN, A regularity resuit for the Stokes problem in a convex polygon, J Funct Anal 21, pp 397-431, 1976 Zbl0317.35037MR404849
  12. 12 O LADYZHENSKAYA, The mathematical theory of viscous incompressible flows, Gordon & Breach, 1963 Zbl0121.42701MR155093
  13. 13 R TEMAM, Navier-Stokes equations, North Holland Publishing Company, 1977 Zbl0426.35003MR603444

Citations in EuDML Documents

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  1. P. Peisker, On the numerical solution of the first biharmonic equation
  2. Petr Knobloch, Lutz Tobiska, Stabilization methods of bubble type for the Q 1 / Q 1 -element applied to the incompressible Navier-Stokes equations
  3. Jean Luc Guermond, Peter D. Minev, Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case
  4. Petr Knobloch, Lutz Tobiska, Stabilization methods of bubble type for the -element applied to the incompressible Navier-Stokes equations
  5. Jean Luc Guermond, Peter D. Minev, Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
  6. Richard S. Falk, A Fortin operator for two-dimensional Taylor-Hood elements
  7. Aihui Zhou, Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
  8. Christine Bernardi, Frédéric Hecht, More pressure in the finite element discretization of the Stokes problem
  9. O. Goubet, Separation of variables in the Stokes problem application to its finite element multiscale approximation
  10. R. Verfürth, Finite element approximation of steady Navier-Stokes equations with mixed boundary conditions

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