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

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.

References in corpus (2)

• Climate dynamics and fluid mechanics: Natural variability and related uncertainties
• Approximate deconvolution large eddy simulation of a barotropic ocean circulation model

Cited by in corpus (5)

• A Two-Level Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean
• Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
• A fast time-stepping strategy for dynamical systems equipped with a surrogate model
• Convergence of a steepest descent algorithm in shape optimisation using $W^{1,\infty }$ functions
• Stable $C^1$-conforming finite element methods for a class of nonlinear fourth-order evolution equations