A Conforming Finite Element Discretization of the Streamfunction Form of the Unsteady Quasi-Geostrophic Equations

TL;DR

This paper introduces a conforming finite element method for the unsteady quasi-geostrophic equations' streamfunction form, providing optimal error estimates and numerical validation for modeling large-scale ocean circulation.

Contribution

It develops a new finite element discretization for the unsteady quasi-geostrophic equations with proven optimal error bounds.

Findings

Optimal error estimates derived

Numerical results confirm theoretical accuracy

Method effectively models large-scale ocean circulation

Abstract

This paper presents a conforming finite element semi-discretization of the streamfunction form of the one-layer unsteady quasi-geostrophic equations, which are a commonly used model for large-scale wind-driven ocean circulation. We derive optimal error estimates and present numerical results.