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

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.