Error estimates of B-spline based finite-element methods for the stationary quasi-geostrophic equations of the ocean

Dohyun Kim, Tae Yeon Kim, Eun-Jae Park, Dong wook Shin

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper presents theoretical error estimates of B-spline based finite-element methods for the streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. We introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous Galerkin method. Dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via Nitsche's method. Existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption. Numerical experiments are performed to verify the theoretical error estimates on rectangular and L-shape geometries.

Original languageEnglish
Pages (from-to)255-272
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Volume335
DOIs
Publication statusPublished - 2018 Jun 15

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splines
Splines
finite element method
oceans
Finite element method
formulations
estimates
Galerkin methods
Galerkin method
uniqueness
Stabilization
penalties
norms
Boundary conditions
Geometry
stabilization
boundary conditions
geometry
Experiments
approximation

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 theoretical error estimates of B-spline based finite-element methods for the streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. We introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous Galerkin method. Dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via Nitsche's method. Existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption. Numerical experiments are performed to verify the theoretical error estimates on rectangular and L-shape geometries.",
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Error estimates of B-spline based finite-element methods for the stationary quasi-geostrophic equations of the ocean. / Kim, Dohyun; Kim, Tae Yeon; Park, Eun-Jae; Shin, Dong wook.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 335, 15.06.2018, p. 255-272.

Research output: Contribution to journalArticle

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AB - This paper presents theoretical error estimates of B-spline based finite-element methods for the streamfunction formulation of the stationary quasi-geostrophic equations, which describe the large scale wind-driven ocean circulation. We introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous Galerkin method. Dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via Nitsche's method. Existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption. Numerical experiments are performed to verify the theoretical error estimates on rectangular and L-shape geometries.

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