A second-order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

A fully discrete second-order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second-order decoupled implicit/explicit scheme is used for time discretization, and a finite element method based on the P-1 (P-1) - P-1 - P-1 (P-1) elements for velocity, pressure and density is used for spatial discretization of these primitive equations. Optimal H-1 - L-2 - H-1 error estimates for numerical solution (u(h)(n), p(h)(n), theta(n)(h)) and an optimal L-2 error estimate for (u(h)(n), theta(n)(h)) are established under the convergence condition of 0 < h <= beta(1), 0 < tau <= beta(2), and tau <= beta(3)h for some positive constants beta(1), beta(2), and beta(3). Furthermore, numerical computations show that the H-1 - L-2 - H-1 convergence rate for numerical solution (u(h)(n), p(h)(n), theta(n)(h)) is of O (h + tau(2)) and an L-2 convergence rate for (u(h)(n), theta(n)(h)) is O (h(2) + tau(2)) with the assumed convergence condition, where h is a mesh size and tau is a time step size. More practical calculations are performed as a further validation of the numerical method. Copyright (C) 2016 John Wiley & Sons, Ltd.