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Error Analysis of a B-Spline Based Finite-Element Method for Modeling Wind-Driven Ocean Circulation

Abstract

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.

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Acknowledgments

The work has been partially supported by (N.R.) ERC-2010-AdG No. 267802 Analysis of Multiscale Systems Driven by Functionals, and by (L.H.) project OpenViewSHIP, “Sviluppo di un ecosistema computazionale per la progettazione idrodinamica del sistema elica-carena”, supported by Regione FVG - PAR FSC 2007–2013, Fondo per lo Sviluppo e la Coesione and by the project “TRIM – Tecnologia e Ricerca Industriale per la Mobilità Marina”, CTN01-00176-163601, supported by MIUR, the Italian Ministry of Instruction, University and Research. E.F. gratefully acknowledges support from the Okinawa Institute of Science and Technology Graduate University with subsidy funding from the Cabinet Office, Government of Japan.

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Correspondence to Eliot Fried.

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Rotundo, N., Kim, TY., Jiang, W. et al. Error Analysis of a B-Spline Based Finite-Element Method for Modeling Wind-Driven Ocean Circulation. J Sci Comput 69, 430–459 (2016). https://doi.org/10.1007/s10915-016-0201-1

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Keywords

  • Quasigeostrophic equations
  • Stream function
  • Vorticity
  • Nitsche’s method
  • Optimal convergence

Mathematics Subject Classification

  • 65M15
  • 65D07
  • 74S05