Journal of Scientific Computing

, Volume 69, Issue 1, pp 430–459 | Cite as

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

  • Nella Rotundo
  • Tae-Yeon Kim
  • Wen Jiang
  • Luca Heltai
  • Eliot FriedEmail author


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.


Quasigeostrophic equations Stream function Vorticity  Nitsche’s method Optimal convergence 

Mathematics Subject Classification

65M15 65D07 74S05 



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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Nella Rotundo
    • 1
  • Tae-Yeon Kim
    • 2
  • Wen Jiang
    • 3
  • Luca Heltai
    • 4
  • Eliot Fried
    • 5
    Email author
  1. 1.Weierstraß-InstitutBerlinGermany
  2. 2.Civil Infrastructure and Environmental EngineeringKhalifa UniversityAbu DhabiUAE
  3. 3.Fuels Modeling and SimulationIdaho National LaboratoryIdaho FallsUSA
  4. 4.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  5. 5.Mathematical Soft Matter UnitOkinawa Institute of Science and Technology Graduate UniversityOnnaJapan

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