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First order decoupled method of the primitive equations of the ocean: I: Time discretization. (English) Zbl 1308.65143
Summary: In this article, we study the time discretization of the first order decoupled semi-implicit scheme of the 3D primitive equations of the ocean in the case of the non-slip and non-heat flux boundary conditions on the side. The almost unconditional stability of the scheme and the optimal error estimates of the time discrete velocity, pressure and density are provided.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q86 PDEs in connection with geophysics
86A05 Hydrology, hydrography, oceanography
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