B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

We present a B-spline based conforming finite-element method of the streamfunction formulation of the stationary one-layer quasi-geostrophic equations for the study of the large scale wind-driven ocean circulation. The method encompasses standard simplifications of these equations, in particular the linear Stommel and Stommel–Munk models. A variational form of the method is developed and its consistency is established. In this formulation Dirichlet boundary conditions are enforced only weakly and stabilization is achieved via Nitsche’s method. Stability parameters are evaluated by solving a local generalized eigenvalue problem on the Dirichlet boundary and by monitoring the condition number of the resulting linear systems. Comparisons of the results from our simulations with previously published results and convergence studies lead us to conclude that our finite-element discretization is accurate.