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 | |
| Publication status | Published - 2018 Jun 15 |
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All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications
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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 journal › Article
TY - JOUR
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
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.
UR - http://www.scopus.com/inward/record.url?scp=85043594478&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85043594478&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.02.009
DO - 10.1016/j.cma.2018.02.009
M3 - Article
AN - SCOPUS:85043594478
VL - 335
SP - 255
EP - 272
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
ER -