Geodesic
On the convergence of difference schemes for the equations of ocean dynamics
Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1091-1111 Cet article a éte moissonné depuis la source Math-Net.Ru

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The difference scheme which approximates the equations of large-scale ocean dynamics in a unit cube to the second degree in the space variables is investigated. It is shown that the solutions converge to the solution of the differential problem. Namely, under the assumption that the solution is sufficiently smooth it is proved that $$ \max_{0\le m\le M}\|{\mathbf u}(m\tau)-{\mathbf v}^m\|=O(\tau+h^{3/2}), \qquad M\tau=T, $$ where $\|\cdot\|$ is the grid $L_2$-norm with respect to the space variables, $\mathbf v$ is the solution of the grid problem, and $\mathbf u$ is the solution of the differential problem. Bibliography: 7 titles.
Keywords: primitive equations, equations of ocean dynamics, nonlinear partial differential equations, finite-difference scheme
Mots-clés : convergence. 
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A. V. Drutsa; G. M. Kobel'kov. On the convergence of difference schemes for the equations of ocean dynamics. Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1091-1111. http://geodesic.mathdoc.fr/item/SM_2012_203_8_a1/

[1] V. L. Zotov, “A difference scheme for a set of equations of the atmosphere dynamics”, Moscow Univ. Comput. Math. Cybernet., 1988, no. 1, 14–22 | MR | Zbl

[2] G. M. Kobelkov, “Global existence of a solution to the ocean dynamics equations”, Dokl. Math., 73:2 (2006), 296–298 | DOI | MR

[3] G. M. Kobelkov, “Existence of a solution “in the large” for the 3D large-scale ocean dynamics equations”, C. R. Math. Acad. Sci. Paris, 343:4 (2006), 283–286 | DOI | MR | Zbl

[4] G. M. Kobelkov, “Existence of a solution “in the large” for ocean dynamics equations”, J. Math. Fluid Mech., 9:4 (2007), 588–610 | DOI | MR | Zbl

[5] A. V. Drutsa, “Existence “in the large” of a solution to primitive equations in a domain with uneven bottom”, Russian J. Numer. Anal. Math. Modelling, 24:6 (2009), 515–542 | DOI | MR | Zbl

[6] C. Cao, E. S. Titi, “Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics”, Ann. of Math. (2), 166:1 (2007), 245–267 | DOI | MR | Zbl

[7] V. I. Lebedev, “Metod konechnykh setok dlya uravnenii tipa S. L. Soboleva”, Dokl. AN SSSR, 114:6 (1957), 1166–1169 | MR | Zbl