Geodesic
$V$-cycle multi-grid method of viscoelastic fluid flow obeying an Oldroyd-B-type constitutive law
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 83-94 
Zuliang Lu; Hongwei Zhang. $V$-cycle multi-grid method of viscoelastic fluid flow obeying an Oldroyd-B-type constitutive law. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/SJVM_2008_11_1_a6/
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     title = {$V$-cycle multi-grid method of viscoelastic fluid flow obeying an {Oldroyd-B-type} constitutive law},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the time-dependent viscoelastic fluid flow obeying an Oldroyd B type constitutive law in three dimensional domains, we put forward a $V$-cycle multi-grid method. At the same time, we discuss existence, uniqueness and error estimates of the approximate solution. The approximate stress, velocity and pressure are, respectively, $\sigma_k$ discontinuous, $u_k$ continuous, $p_k$ continuous.

[1] Xu J., “A Novel Two-Grid Method for Semilinear Equations”, SIAM J. Sci. Comput., 15 (1994), 231–237 | DOI | MR | Zbl

[2] Xu J., “Two-Grid Discretization Techniques for Linear and Non-Linear PDEs”, SIAM J. Num. Anal., 33 (1996), 1759–1777 | DOI | MR | Zbl

[3] Chen Y., Huang Y. Q., and Yu D., “A Two-Grid Method for Expanded Mixed Finite-Element Solution of Semilinear Reaction-Diffusion Equations”, Nat. Sci. J. Xiangtan Univ., 24 (2002), 101–124

[4] Dawson C. N. and Wheeler M. F., “Two-Grid Methods for Mixed Finite Element Approximations of Non-Linear Parabolic Equations”, Contemp. Math., 180 (1994), 191–203 | MR | Zbl

[5] Brenner S. C. and Scott L. R., The Mathematical Theory of Finite Element Methods, Springer-Verlag, 1994 | MR

[6] Baranger J. and Sandri D., “Finite Element Approximation of Viscoelastic Fluid Flow: Existence of Approximate Solutions and Error Bounds”, Num. Math., 63 (1992), 13–27 | DOI | MR | Zbl

[7] Sandri D., “Finite Element Approximation of Viscoelastic Fluid Flow: Existence of Approximate Solutions and Error Bounds. II. Continuous Approximation of the Stress”, SIAM J. Num. Anal., 31 (1994), 362–377 | DOI | MR | Zbl

[8] Zhang Hongwei and Lu Zuliang, “Mixed Finite Element Method of Viscoelastic Fluid Flow”, J. Changsha Univ. Electric Power, 4 (2006), 36–44

[9] Adams R. A., Sobolev Spaces, Academic Press, New York, 1975 | MR | Zbl

[10] Layton W. J., “A Two-Level Discretization Method for the Navier–Stokes Equations”, Comput. Math. Appl., 26:2 (1993), 31–38 | DOI | MR