A Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean

TL;DR

This paper develops a finite element method for the stationary quasi-geostrophic equations in ocean modeling, providing optimal error estimates and validating accuracy through numerical tests against standard models.

Contribution

It introduces a conforming finite element discretization with proven optimal error estimates for the streamfunction formulation of the quasi-geostrophic equations.

Findings

Finite element discretization achieves optimal error bounds.

Numerical results match theoretical convergence rates.

Method accurately models large-scale ocean circulation.

Abstract

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.