A numerical solver for the primitive equations of the ocean using term-by-term stabilization

In this work we introduce and analyze a numerical approximation of the primitive equations of the ocean by means of stabilized finite elements. We use a reduced formulation of these equations which only includes the (3D) horizontal velocity and the (2D) surface pressure. This, combined with the use of stabilized finite elements, provides a large reduction of degrees of freedom in comparison with previous mixed methods. The use of isoparametric prismatic finite elements provides good geometric adaptability to the topography. We perform an analysis of stability and convergence using the concept of static condensation on bubble spaces. Finally, we test our stabilized approximations in flows with complex 3D structure, including a real-life application. Specifically, we simulate the wind-driven circulation in Lake Neuchaˆtel.