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

doi:10.1016/j.cma.2018.02.009

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

Department of Computational Science and Engineering

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

5 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 language	English
Pages (from-to)	255-272
Number of pages	18
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	335
DOIs	https://doi.org/10.1016/j.cma.2018.02.009
Publication status	Published - 2018 Jun 15

Bibliographical note

Funding Information:
The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103). The third author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358.

Funding Information:
The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103 ). The third author was supported by NRF - 2015R1A5A1009350 and NRF- 2016R1A2B4014358 .

Publisher Copyright:
© 2018 Elsevier B.V.

All Science Journal Classification (ASJC) codes

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

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10.1016/j.cma.2018.02.009

Cite this

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

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.",

author = "Dohyun Kim and Kim, {Tae Yeon} and Park, {Eun Jae} and Shin, {Dong wook}",

note = "Funding Information: The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103). The third author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Funding Information: The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103 ). The third author was supported by NRF - 2015R1A5A1009350 and NRF- 2016R1A2B4014358 . Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = jun,

day = "15",

doi = "10.1016/j.cma.2018.02.009",

language = "English",

volume = "335",

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journal = "Computer Methods in Applied Mechanics and Engineering",

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T1 - Error estimates of B-spline based finite-element methods for the stationary quasi-geostrophic equations of the ocean

AU - Kim, Dohyun

AU - Kim, Tae Yeon

AU - Park, Eun Jae

AU - Shin, Dong wook

N1 - Funding Information: The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103). The third author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Funding Information: The second author was supported by the ADEK Award for Research Excellence (AARE) 2017 (No. 8434000103 ). The third author was supported by NRF - 2015R1A5A1009350 and NRF- 2016R1A2B4014358 . Publisher Copyright: © 2018 Elsevier B.V.

PY - 2018/6/15

Y1 - 2018/6/15

N2 - 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.

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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EP - 272

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -

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

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