C0-discontinuous Galerkin methods for a wind-driven ocean circulation model: Two-grid algorithm

Dong wook Shin, Younghun Kang, Eun-Jae Park

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents a nonconforming finite element method for a streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. The streamfunction formulation is a fourth order nonlinear PDE and the nonconforming method is based on C0-elements instead of C1-elements. Existence and uniqueness of the approximation are proved and optimal error estimates in several norms of interest are demonstrated under a small data assumption. Two-grid algorithms based on Picard and Newton type linearizations are then presented to efficiently resolve nonlinearities and computational results are given to demonstrate the efficiency of the algorithm. The Mediterranean sea example is tested with real world coastline data, which illustrates the effectiveness of the two-grid approach in the wind-driven ocean circulation simulation.

Original languageEnglish
Pages (from-to)321-339
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume328
DOIs
Publication statusPublished - 2018 Jan 1

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Galerkin method
Galerkin methods
oceans
grids
formulations
Mediterranean Sea
pulse detonation engines
linearization
uniqueness
Linearization
norms
newton
finite element method
nonlinearity
Finite element method
estimates
approximation
simulation

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

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abstract = "This paper presents a nonconforming finite element method for a streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. The streamfunction formulation is a fourth order nonlinear PDE and the nonconforming method is based on C0-elements instead of C1-elements. Existence and uniqueness of the approximation are proved and optimal error estimates in several norms of interest are demonstrated under a small data assumption. Two-grid algorithms based on Picard and Newton type linearizations are then presented to efficiently resolve nonlinearities and computational results are given to demonstrate the efficiency of the algorithm. The Mediterranean sea example is tested with real world coastline data, which illustrates the effectiveness of the two-grid approach in the wind-driven ocean circulation simulation.",
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C0-discontinuous Galerkin methods for a wind-driven ocean circulation model : Two-grid algorithm. / Shin, Dong wook; Kang, Younghun; Park, Eun-Jae.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 328, 01.01.2018, p. 321-339.

Research output: Contribution to journalArticle

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AU - Park, Eun-Jae

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