First-order decoupled method of the three-dimensional primitive equations of the ocean

Abstract

This paper is concerned with a first-order fully discrete decoupled method for solving the three-dimensional (3D) primitive equations of the ocean with the Dirichlet boundary conditions on the side, where a decoupled semi-implicit scheme is used for the time discretization, and the $P_1(P_1)-P_1-P_1(P_1)$ finite element for velocity, pressure, and density is used for the spatial discretization of these equations. The $H^1-L^2-H^1$ optimal error estimates for the numerical solution $(u_h^n,p_h^n,\theta_h^n)$ and the $L^2$ optimal error estimate for $(u^n_h,\theta_h^n)$ are established under the restriction of $0