A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

Abstract

We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with Dörfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.