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 Fried

doi:10.1007/s10915-016-0201-1

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 Fried

Civil & Environmental Engineering

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	British English
Pages (from-to)	430-459
Number of pages	30
Journal	Journal of Scientific Computing
Volume	69
Issue number	1
DOIs	https://doi.org/10.1007/s10915-016-0201-1
State	Published - 1 Oct 2016

Keywords

Nitsche’s method
Optimal convergence
Quasigeostrophic equations
Stream function
Vorticity

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title = "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.",

keywords = "Nitsche{\textquoteright}s method, Optimal convergence, Quasigeostrophic equations, Stream function, Vorticity",

author = "Nella Rotundo and Kim, \{Tae Yeon\} and Wen Jiang and Luca Heltai and Eliot Fried",

note = "Funding Information: 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 Mobilit{\`a} 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. Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

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AU - Fried, Eliot

N1 - Funding Information: 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. Publisher Copyright: © 2016, Springer Science+Business Media New York.

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N2 - 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.

AB - 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.

KW - Nitsche’s method

KW - Optimal convergence

KW - Quasigeostrophic equations

KW - Stream function

KW - Vorticity

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

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