Morley finite element methods for the stationary quasi-geostrophic equation

Dohyun Kim, Amiya K. Pani, Eun Jae Park

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1 Citation (Scopus)

Abstract

In this paper, we propose and analyze a nonconforming Morley finite element method for the stationary quasi-geostrophic equation in the ocean circulation. Stability and the inf–sup condition for the discrete solution are proved, and the local existence of a unique solution to the discrete nonlinear system is established based on the assumption of the existence of an isolated solution to the linearized problem and Banach fixed point argument. One principal tool employed is to exploit the enrichment operator from nonconforming space to H02(Ω). Thereby, not only smallness assumption on data is avoided, but also optimal error estimates in H2- and H1-norms are proved under minimal regularity condition on the exact solution. Then, for the nonlinear discrete system, the Newton method is applied, which is shown to preserve local quadratic convergence. Moreover, a posteriori error estimator for an adaptive algorithm is derived. Finally, several numerical experiments with a benchmark problem are considered to confirm our theoretical findings.

Original languageEnglish
Article number113639
JournalComputer Methods in Applied Mechanics and Engineering
Volume375
DOIs
Publication statusPublished - 2021 Mar 1

Bibliographical note

Funding Information:
This author was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021).

Publisher Copyright:
© 2020 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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