Second Order Decoupled Implicit/Explicit Method of the Primitive Equations of the Ocean I: Time Discretization

Abstract

In this article, we propose the time discretization of the second order decoupled implicit/explicit method of the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side. We deduce the second order optimal error estimates on the $L^2$ and $H^1$ norms of the time discrete velocity and density and the $L^2$ norm of the time discrete pressure under the restriction of the time step $0<\tau\leq\beta$ for some positive constant $\beta$. Also, we deduce some stability results on the time discrete solution under the same restriction on the time step.