A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

Ibrahim Al Balushi; Wen Jiang; Gantumur Tsogtgerel; Tae Yeon Kim

doi:10.1016/j.cma.2020.113317

A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

Ibrahim Al Balushi, Wen Jiang, Gantumur Tsogtgerel, Tae Yeon Kim

Civil & Environmental Engineering

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

2 Scopus citations

Abstract

We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with Dörfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.

Original language	British English
Article number	113317
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	371
DOIs	https://doi.org/10.1016/j.cma.2020.113317
State	Published - 1 Nov 2020

Keywords

Adaptivity
Continuous/Discontinuous Galerkin
Nitsche's method
Ocean circulation

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10.1016/j.cma.2020.113317

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title = "A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean",

abstract = "We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with D{\"o}rfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.",

keywords = "Adaptivity, Continuous/Discontinuous Galerkin, Nitsche's method, Ocean circulation",

author = "{Al Balushi}, Ibrahim and Wen Jiang and Gantumur Tsogtgerel and Kim, {Tae Yeon}",

note = "Funding Information: We thank Emmanuil Georgoulis for discussion about discontinuous-Galerkin methods and his invaluable advice. T.-Y. Kim gratefully appreciates the support from Khalifa University Internal Research Funding ( CIRA-2019-009 , No. 8474000170 ). Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

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T1 - A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

AU - Al Balushi, Ibrahim

AU - Jiang, Wen

AU - Tsogtgerel, Gantumur

AU - Kim, Tae Yeon

N1 - Funding Information: We thank Emmanuil Georgoulis for discussion about discontinuous-Galerkin methods and his invaluable advice. T.-Y. Kim gratefully appreciates the support from Khalifa University Internal Research Funding ( CIRA-2019-009 , No. 8474000170 ). Publisher Copyright: © 2020 Elsevier B.V.

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with Dörfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.

AB - We provide a posteriori error analysis of a B-spline based finite-element method for the streamfunction formulation of the stationary quasi-geostrophic equations to model the large scale wind-driven ocean circulation. The analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries. To verify the capability of the error estimator, we use hierarchical B-splines in conjunction with Dörfler marking strategy. Numerical studies are performed for several benchmark examples on rectangular and L-shape ocean geometries.

KW - Adaptivity

KW - Continuous/Discontinuous Galerkin

KW - Nitsche's method

KW - Ocean circulation

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DO - 10.1016/j.cma.2020.113317

M3 - Article

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 113317

ER -

A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean

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Keywords

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