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. © 2013 Elsevier Inc.
He, Y. (2014). First order decoupled method of the primitive equations of the ocean I: Time discretization. Journal of Mathematical Analysis and Applications, 412(2), 895–921. https://doi.org/10.1016/j.jmaa.2013.11.013