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On the shallow water equations at low Reynolds number. (English) Zbl 0723.76033

A functional-analytic investigation of the shallow water equations for low Reynolds number, i.e. for the linearized form is presented. Existence of a solution is discussed for various formulations of the viscous term. A time implicit FEM is proposed and analyzed. In the appendix a rigorous derivation of the shallow water equation is presented.

MSC:

76D33 Waves for incompressible viscous fluids
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A15 Variational methods applied to PDEs
35M20 PDE of composite type (MSC2000)
76D99 Incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics

Software:

TELEMAC
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References:

[1] DOI: 10.1007/BF02576171 · Zbl 0593.76039
[2] Brezzi F., Fast elliptic solver GAMM Workshop (1975)
[3] Baker A. J., Proc. Seminar on finite Element Flow Analysis (1989)
[4] DOI: 10.1016/0045-7825(90)90170-Q · Zbl 0725.65106
[5] Benque J. -P., Pitman (1982)
[6] Berestycki H., Thése de 3éme cycle (1975)
[7] Berg, J. and Löfström, J. 1976. ”Interpolation Spaces: an Introduction”. Springer-Verlag.
[8] Brezzi F., R.A.I.R.O. Anal. NUmér. 8 pp 129– (1973)
[9] cahouét J., rapport.E.D.F 8 pp 85– (1985)
[10] J .C. Galland, N. Goutal and J.M. Hervouet –Telemac A new numberical model for solving shallow water equations, in Advances in Water Resources
[11] Girault V., Theory and Algorithms · Zbl 0296.65049
[12] Goutal N., Thé Université Pierre et Matie Curie (1987)
[13] Hervouet J.–M., Théorie etmise en oevre informatique (1987)
[14] DOI: 10.1002/fld.1650020106 · Zbl 0483.76023
[15] DOI: 10.1002/fld.1650060605 · Zbl 0597.76014
[16] Lions J.–L., ProBlémes aux limites non homogénes et applciation 1 (1986)
[17] Pierre G., I.N.I.R.A. Report 657 (198)
[18] Pinder, G. and Gray, W. 1977. ”–Finite Element simulaitons in surface and subsurface Hydrology”. Academic Press.
[19] O. Pironneau Méthods des éléments finis pour les fludies Masson (1988) and Wiley (1989) for the English translation
[20] DOI: 10.1016/0899-8248(89)90026-8 · Zbl 0702.76073
[21] Stampacchia G., Ann. Inst. fourier Grenoble 15 pp 189– (1965) · Zbl 0151.15401
[22] DOI: 10.1007/BF02418013 · Zbl 0353.46018
[23] Temam R., Theory and Numerical Analysis (1977) · Zbl 0383.35057
[24] Valli A., Ann. Scuola Norm. sup. Pisa. 10 pp 607– (1983)
[25] Valli A., Ann. Inst. Henri Poincaré 4 pp 99– (1987)
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