Calendar Details

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Thursday, November 15

Finite Elements for the Quasi-Geostrophic
Equations of the Ocean

Erich Foster, Virginia Polytechnic Institute and State University, Blacksburg
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Joint Institute for Computational Sciences (Building 5100), Auditorium (Room 128)
Contact: Clayton Webster (webstercg@ornl.gov), 865.574.3649

Abstract

Erich Foster will present a conforming finite element (FE) discretization of the stream function formulation of the pure stream function form of the quasi-geostrophic equations (QGE), which are a commonly used model for the large scale wind-driven ocean circulation. The pure stream function form of the QGE is a fourth-order PDE and therefore requires a C^1 FE discretization to be conforming. Thus, the Argyris finite element, a C^1 FE with 21 degrees of freedom, was chosen for the FE discretization of the QGE. Optimal error estimates for the pure stream function form of the QGE will be presented. The QGE is a simplified model of the ocean, however it can be computationally expensive to resolve all scales, therefore numerical methods, such as the two-level method, are indispensable for time sensitive projects. A two-level method and optimal error estimate for a two-level method applied to the conforming FE discretization of the pure stream function form of the QGE will be presented and computational efficiency will be demonstrated