We present the results of an error analysis of a B-spline based finite-element approximation
of the stream-function formulation of the large scale wind-driven ocean circulation. In
particular, we derive optimal error estimates for h-refinement using a Nitsche-type variational
formulations of the two simplied linear models of the stationary quasigeostrophic equations,
namely the Stommel and Stommel–Munk models. Numerical results obtained from
simulations performed on rectangular and embedded geometries confirm the error analysis.

This paper presents an adaptive refinement algorithm of a B-spline based finite-element
approximation of the streamfunction formulation for the large scale wind-driven ocean
currents. In particular, we focus on a posteriori error analysis of the simplified linear model of
the stationary quasi-geostrophic equations, namely the Stommel–Munk model, which is the
fourth-order partial differential equation. The analysis provides a posteriori error estimator for
the local refinement of the Nitsche-type finite-element formulation. Numerical experiments …