A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow
M2AN - Modélisation mathématique et analyse numérique, Volume 26 (1992) no. 2, pp. 331-345.
@article{M2AN_1992__26_2_331_0,
author = {Baranger, J. and Sandri, D.},
title = {A formulation of {Stokes's} problem and the linear elasticity equations suggested by the {Oldroyd} model for viscoelastic flow},
journal = {M2AN - Mod\'elisation math\'ematique et analyse num\'erique},
pages = {331--345},
publisher = {AFCET - Gauthier-Villars},
volume = {26},
number = {2},
year = {1992},
zbl = {0738.76002},
mrnumber = {1153005},
language = {en},
url = {http://www.numdam.org/item/M2AN_1992__26_2_331_0/}
}
TY  - JOUR
AU  - Baranger, J.
AU  - Sandri, D.
TI  - A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow
JO  - M2AN - Modélisation mathématique et analyse numérique
PY  - 1992
DA  - 1992///
SP  - 331
EP  - 345
VL  - 26
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1992__26_2_331_0/
UR  - https://zbmath.org/?q=an%3A0738.76002
UR  - https://www.ams.org/mathscinet-getitem?mr=1153005
LA  - en
ID  - M2AN_1992__26_2_331_0
ER  - 
%0 Journal Article
%A Baranger, J.
%A Sandri, D.
%T A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow
%J M2AN - Modélisation mathématique et analyse numérique
%D 1992
%P 331-345
%V 26
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%G en
%F M2AN_1992__26_2_331_0
Baranger, J.; Sandri, D. A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow. M2AN - Modélisation mathématique et analyse numérique, Volume 26 (1992) no. 2, pp. 331-345. http://www.numdam.org/item/M2AN_1992__26_2_331_0/

[1] D. N. Arnold, J. Douglas and C. P. Gupta, A Family of Higher Order Mixed Finite Element Methods for Plane Elasticity, Numer. Math., 45, 1-22 (1984). | MR | Zbl

[2] I. Babuska, Error-bounds for Finite Element Method, Numer. Math., 16, 322-333 (1971). | MR | Zbl

[3] F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Model. Math. Anal. Numér., 8, 129-151 (1974). | Numdam | MR | Zbl

[4] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland (1978). | MR | Zbl

[5] P. Clement, Approximation by finite elements using local regularization, RAIRO Modél. Math. Anal. Numér., 8, 77-84 (1975). | Numdam | MR | Zbl

[6] J. Douglas and J. Wang, An absolutely stabilized finite element method for the Stokes problem, quoted in [12]. | Zbl

[7] M. Fortin and A. Fortin, A new approach for the FEM simulation of viscoelastic flows, J. Non-Newtonian Fluid Mech., 32, 295-310 (1989). | Zbl

[8] M. Fortin and R. Pierre, On the convergence of the mixed method of Crochetand Marchal for viscoelastic flows, to appear. | MR | Zbl

[9] L. P. Franca, Analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle, Comp. Meth. Appl. Mech. Engrg., 76, 259-273 (1989). | MR | Zbl

[10] L. P. Franca and T. J. R. Hughes, Two classes of mixed finite element methods, Comp. Meth. Appl. Mech. Engrg., 69, 89-129 (1988). | MR | Zbl

[11] L. P. Franca, R. Stenberg, Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity, to appear in Appl. Mech. Rev. | MR | Zbl

[12] L.P. Franca and R. Stenberg, Error analysis of some Galerkin-least-squares methods for the elasticity equations, Rapport INRIA, n° 1054 (1989). | Zbl

[13] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and algorithms, Springer Berlin (1978). | MR | Zbl

[14] J. M. Marchal and M. J. Crochet, A new mixed finite element for calculating viscoelastic flow, J. Non-Newtonian Fluid Mech., 26, 77-114 (1987). | Zbl

[15] L. R. Scott and M. Vogelius, Norm estimates for a maximal right inverse ofthe divergence operator in spaces of piecewise polynomials, RAIRO Modél. Math. Anal. Numér., 19, 111-143 (1985). | Numdam | MR | Zbl

[16] R. Stenberg, A Family of Mixed Finite Elements for the Elasticity Problem, Num. Math., 53, 513-538 (1988). | MR | Zbl

[17] R. Stenberg, Error Analysis of some Finite Element Methods for the Stokes Problem, to appear. | MR | Zbl