Local error estimates for finite element discretization of the Stokes equations
Arnold, Douglas N. ; Xiaobo, Liu
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995), p. 367-389 / Harvested from Numdam
Publié le : 1995-01-01
@article{M2AN_1995__29_3_367_0,
     author = {Arnold, Douglas N. and Xiaobo, Liu},
     title = {Local error estimates for finite element discretization of the Stokes equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {29},
     year = {1995},
     pages = {367-389},
     mrnumber = {1342712},
     zbl = {0832.65117},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1995__29_3_367_0}
}
Arnold, Douglas N.; Xiaobo, Liu. Local error estimates for finite element discretization of the Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995) pp. 367-389. http://gdmltest.u-ga.fr/item/M2AN_1995__29_3_367_0/

[1] D. N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokes equations, Calcolo, 21, 1984, pp. 337-344. | MR 799997 | Zbl 0593.76039

[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. | MR 1025088 | Zbl 0696.73040

[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. | Numdam | MR 343661 | Zbl 0302.65087

[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. | MR 977489 | Zbl 0681.35071

[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. | Numdam | MR 807324 | Zbl 0613.65110

[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] L. Gastaldi, Uniform interior error estimates for the Reissner-Mindlin plate model, Math. Comp., 61, 1993, pp. 539-567. | MR 1185245 | Zbl 0784.73046

[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. | MR 339677 | Zbl 0328.76020

[9] L. Mansfield, Finite element subspaces with optimal rates of convergence for stationary Stokes problem, RAIRO Anal. Numér., 16, 1982, pp. 49-66. | Numdam | MR 648745 | Zbl 0477.65084

[10] J. A. Nltsche and A. H. Schatz, Interior estimate for Ritz-Galerkin methods, Math. Comp., 28, 1974, pp. 937-958. | MR 373325 | Zbl 0298.65071

[11] R. Témam, Navier-Stokes Equations, North-Holland, Amsterdam, 1984. | MR 769654 | Zbl 0568.35002

[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. | MR 1115238 | Zbl 0875.65089