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.
|Number of pages||18|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2018 Jun 15|
Bibliographical noteFunding 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.
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 .
© 2018 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications