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

TL;DR

This paper introduces a two-level finite element method for the stationary quasi-geostrophic equations, providing optimal error estimates and demonstrating computational efficiency improvements through numerical experiments.

Contribution

It presents a novel two-level finite element discretization with proven error bounds and efficiency benefits for modeling large-scale ocean circulation.

Findings

Optimal error estimates were derived for the discretization.

Numerical experiments confirmed theoretical error bounds.

The two-level algorithm reduces computational time significantly.

Abstract

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.