Geodesic
On the convergence of difference schemes for the equations of ocean dynamics
Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1091-1111

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2012_203_8_a1,
     author = {A. V. Drutsa and G. M. Kobel'kov},
     title = {On the convergence of difference schemes for the equations of ocean dynamics},
     journal = {Sbornik. Mathematics},
     pages = {1091--1111},
     publisher = {mathdoc},
     volume = {203},
     number = {8},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_8_a1/}
}
TY  - JOUR
AU  - A. V. Drutsa
AU  - G. M. Kobel'kov
TI  - On the convergence of difference schemes for the equations of ocean dynamics
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 1091
EP  - 1111
VL  - 203
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_8_a1/
LA  - en
ID  - SM_2012_203_8_a1
ER  - 
%0 Journal Article
%A A. V. Drutsa
%A G. M. Kobel'kov
%T On the convergence of difference schemes for the equations of ocean dynamics
%J Sbornik. Mathematics
%D 2012
%P 1091-1111
%V 203
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2012_203_8_a1/
%G en
%F SM_2012_203_8_a1
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/