Erich L Foster

Erich L Foster, Traian Iliescu, Zhu Wang

This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation. Optimal error estimates for this finite element discretization with the Argyris element are derived. Numerical tests for the finite element discretization of the quasi-geostrophic equations and two of its standard simplifications (the linear Stommel model and the linear Stommel-Munk model) are carried out. By benchmarking the numerical results against those in the published literature, we conclude that our finite element discretization is accurate. Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates.

Erich L Foster, Traian Iliescu, David Wells

In this paper we proposed a two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation. Optimal error estimates for the two-level finite element discretization were derived. Numerical experiments for the two-level algorithm with the Argyris finite element were also carried out. The numerical results verified the theoretical error estimates and showed that, for the appropriate scaling between the coarse and fine mesh sizes, the two-level algorithm significantly decreases the computational time of the standard one-level algorithm.

Erich L Foster, Jérôme Lohéac, Minh-Binh Tran

In this paper we introduce a numerical scheme which preserves the long time behavior of solutions to the Kolmogorov equation. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov equation into a new form, such that the problem of designing structure preserving schemes, for the original equation, amounts to building a standard scheme for the transformed equation. We also present an analysis for the operator splitting technique for the self-similar method and numerical results for the described scheme.