Mixed formulation of the two-layer quasi-geostrophic equations of the ocean

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

“…In [59,61], Medjo considered this formulation and proved bounds for the time discretization error. Cascon et al [12] proved both a priori and a posteriori error estimates for the FE discretization of the linear Stommel-Munk model, which is a simplified version of the QGE obtained by dropping the nonlinear term.…”

Long-time stability of the implicit Euler scheme for a three dimensional globally modified two-phase flow model

“…This is why we need to use the attractor theory for the so-called multi-valued mappings. Multi-valued dynamical systems have been investigated by many authors (see, e.g., [1,2,6,28,30,31]), but in this article we use the tools developed in [10] (see also [25,26]) to study the convergence of the discrete (multi-valued) attractors to the continuous (single-valued) attractor. For convenience, we recall those results in Section 7.1, and then we apply them to our model in Section 7.2.…”

A Finite element discretization of the streamfunction formulation of the stationary quasi-geostrophic equations of the ocean

“…Indeed, using piecewise polynomials of degree k − 1 for the FE approximation of the vorticity, one would expect an O(h k ) error estimate in the L 2 norm. Medjo [28,29] used a FE discretization of the streamfunction-vorticity formulation and proved error estimates for the time discretization, but no error estimates for the spatial discretization. Finally, Cascon et al [4] proved both a priori and a posteriori error estimates for the FE discretization of the linear Stommel-Munk model (see Section 5.2 for more details).…”