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 journalArticlepeer-review

6 Scopus citations

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 languageBritish English
Pages (from-to)255-272
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Volume335
DOIs
StatePublished - 15 Jun 2018

Keywords

  • B-spline based finite-element
  • Fourth-order partial-differential-equation
  • Nitsche's method
  • Ocean circulation
  • Stabilization
  • Streamfunction

Fingerprint

Dive into the research topics of 'Error estimates of B-spline based finite-element methods for the stationary quasi-geostrophic equations of the ocean'. Together they form a unique fingerprint.

Cite this