A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean. (15th June 2022)

• Record Type: Journal Article
• Authors: Mora, David; Silgado, Alberth
• Is Part Of: Computers & mathematics with applications. Volume 116(2022)
• Page Start: 212
• Page End: 228
• Publication Date: 2022-06-15
• Subjects: Virtual element method -- Quasi-geostrophic equations -- Stream-function formulation -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.05.022
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this present paper, we propose and analyze a C 1 -conforming virtual element method to solve the so-called one-layer stationary quasi-geostrophic equations (QGE) with applications in the large scale wind-driven ocean circulation, formulated in terms of the stream-function. This problem corresponds to a nonlinear fourth order partial differential equation. The C 1 virtual space and the discrete scheme are built in a straightforward way due to the flexibility of the virtual approach. Under the assumption of small data, we prove well-posedness of the discrete problem by using a fixed-point strategy and under standard assumptions on the computational domain, we establish error estimates in H 2 -norm for the stream-function. Finally, we report four numerical experiments that illustrate the behavior of the proposed scheme and confirm our theoretical results on different families of polygonal meshes.