A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 26 (1992) no. 2, p. 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 = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {26},
number = {2},
year = {1992},
pages = {331-345},
zbl = {0738.76002},
mrnumber = {1153005},
language = {en},
url = {http://www.numdam.org/item/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. ESAIM: Mathematical Modelling and Numerical Analysis - 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 761879 | Zbl 0558.73066

[2] I. Babuska, Error-bounds for Finite Element Method, Numer. Math., 16, 322-333 (1971). | MR 288971 | Zbl 0214.42001

[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 365287 | Zbl 0338.90047

[4] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland (1978). | MR 520174 | Zbl 0383.65058

[5] P. Clement, Approximation by finite elements using local regularization, RAIRO Modél. Math. Anal. Numér., 8, 77-84 (1975). | Numdam | MR 400739 | Zbl 0368.65008

[6] J. Douglas and J. Wang, An absolutely stabilized finite element method for the Stokes problem, quoted in [12]. | Zbl 0669.76051

[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 0672.76010

[8] M. Fortin and R. Pierre, On the convergence of the mixed method of Crochetand Marchal for viscoelastic flows, to appear. | MR 1016647 | Zbl 0692.76002

[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 1030385 | Zbl 0688.73044

[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 953593 | Zbl 0629.73053

[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 1037580 | Zbl 0749.73076

[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 0759.73055

[13] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and algorithms, Springer Berlin (1978). | MR 851383 | Zbl 0585.65077

[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 0637.76009

[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 813691 | Zbl 0608.65013

[16] R. Stenberg, A Family of Mixed Finite Elements for the Elasticity Problem, Num. Math., 53, 513-538 (1988). | MR 954768 | Zbl 0632.73063

[17] R. Stenberg, Error Analysis of some Finite Element Methods for the Stokes Problem, to appear. | MR 1010601 | Zbl 0702.65095