Adaptivity of a B-spline based finite-element method for modeling wind-driven ocean circulation

Abstract 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 with several benchmark examples are performed to test the capability of the posteriori error indicator on rectangular and L -shape geometries.

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