Local error estimates for finite element discretization of the Stokes equations

Douglas N. Arnold; Liu Xiaobo

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1995)

  • Volume: 29, Issue: 3, page 367-389
  • ISSN: 0764-583X

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Arnold, Douglas N., and Xiaobo, Liu. "Local error estimates for finite element discretization of the Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.3 (1995): 367-389. <http://eudml.org/doc/193777>.

@article{Arnold1995,
author = {Arnold, Douglas N., Xiaobo, Liu},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {interior error estimates; local error estimates; mixed finite element; stationary Stokes equations; Stokes system},
language = {eng},
number = {3},
pages = {367-389},
publisher = {Dunod},
title = {Local error estimates for finite element discretization of the Stokes equations},
url = {http://eudml.org/doc/193777},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Arnold, Douglas N.
AU - Xiaobo, Liu
TI - Local error estimates for finite element discretization of the Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 3
SP - 367
EP - 389
LA - eng
KW - interior error estimates; local error estimates; mixed finite element; stationary Stokes equations; Stokes system
UR - http://eudml.org/doc/193777
ER -

References

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  1. [1] D. N. ARNOLD, F. BREZZI and M. FORTIN, A stable finite element for the Stokes equations, Calcolo, 21, 1984, pp. 337-344. Zbl0593.76039MR799997
  2. [2] D. N. ARNOLD and R. S. FALK, A uniformly accurate finite element method for the Mindlin-Reissner plate, SIAM J. Numer. Anal, 26, 1989, pp. 1276-1290. Zbl0696.73040MR1025088
  3. [3] M. CROUZEIX and P.-A. RAVIART, Conforming and non-conforming finite element methods for solving the stationary Stokes equations, RAIRO Anal Numér., 7 R-3, 1973, pp. 33-76. Zbl0302.65087MR343661
  4. [4] M. DAUGE, Stationary Stokes and Navier-Stokes Systems on two- or three-dimentional domains with corners. Part I : Linearized equations, SIAM J. Math. Anal., 20, 1989, pp. 74-97. Zbl0681.35071MR977489
  5. [5] J. Jr. DOUGLAS and R. A. MILNER, Interior and superconvergence estimates for mixed methods for second order elliptic problems, RAIRO Modél. Math. Anal. Numér., 19, 1985, pp. 397-428. Zbl0613.65110MR807324
  6. [6] M. FORTIN, Calcul numérique des écoulements des fluides de Bingham et des fluides Newtoniens incompressible par des méthodes d'éléments finis, Université de Paris VI, Doctoral thesis, 1972. 
  7. [7] L. GASTALDI, Uniform interior error estimates for the Reissner-Mindlin plate model, Math. Comp., 61, 1993, pp. 539-567. Zbl0784.73046MR1185245
  8. [8] P. HOOD and C. TAYLOR, A numerical solution of the Navier-Stokes equations using the finite element technique, Compuh & Fluids, 1, 1973, pp. 73-100. Zbl0328.76020MR339677
  9. [9] L. MANSFIELD, Finite element subspaces with optimal rates of convergence for stationary Stokes problem, RAIRO Anal. Numér., 16, 1982, pp. 49-66. Zbl0477.65084MR648745
  10. [10] J. A. NlTSCHE and A. H. SCHATZ, Interior estimate for Ritz-Galerkin methods, Math. Comp., 28, 1974, pp. 937-958. Zbl0298.65071MR373325
  11. [11] R. TÉMAM, Navier-Stokes Equations, North-Holland, Amsterdam, 1984. Zbl0568.35002MR603444
  12. [12] L. B. WAHLBIN, Local Behavior in Finite Element Methods, in Handbook of Numerical Analysis, P. G, Ciarlet and J. L. Lions, eds., Elsevier, Amsterdam-New York, 1991. Zbl0875.65089MR1115238

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