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Mat. Sb., 2012, Volume 203, Number 8, Pages 17–38 (Mi msb7896)  

This article is cited in 4 scientific papers (total in 4 papers)

On the convergence of difference schemes for the equations of ocean dynamics

A. V. Drutsaa, G. M. Kobel'kovab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow

Abstract: 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, convergence.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7896

Full text: PDF file (612 kB)
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English version:
Sbornik: Mathematics, 2012, 203:8, 1091–1111

Bibliographic databases:

UDC: 519.634
MSC: 74S20
Received: 07.06.2011 and 03.02.2012

Citation: A. V. Drutsa, G. M. Kobel'kov, “On the convergence of difference schemes for the equations of ocean dynamics”, Mat. Sb., 203:8 (2012), 17–38; Sb. Math., 203:8 (2012), 1091–1111

Citation in format AMSBIB
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\paper On the convergence of difference schemes for the equations of ocean dynamics
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\pages 17--38
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    This publication is cited in the following articles:
    1. Drutsa A.V., “O poryadke skhodimosti raznostnykh skhem dlya uravnenii dinamiki okeana”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 13:1 (2012), 398–408  mathnet  elib
    2. Stanichenko M.Yu., “Ob odnoi raznostnoi skheme dlya sistemy uravnenii tipa dinamiki atmosfery”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 14:1 (2013), 383–389  mathnet  elib
    3. A. V. Drutsa, “A difference scheme for equations of ocean dynamics on unstructured grids”, Russian J. Numer. Anal. Math. Modelling, 29:3 (2014), 145–165  crossref  mathscinet  zmath  isi  elib  scopus
    4. Temirbekov A.N., Urmashev B.A., Gromaszek K., “Investigation of the Stability and Convergence of Difference Schemes For the Three-Dimensional Equations of the Atmospheric Boundary Layer”, Int. J. Electron. Telecommun., 64:3 (2018), 391–396  crossref  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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