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Mathematics > Numerical Analysis

arXiv:1605.00551 (math)
[Submitted on 2 May 2016 (v1), last revised 13 Oct 2017 (this version, v3)]

Title:Compatible finite element spaces for geophysical fluid dynamics

Authors:Andrea Natale, Jemma Shipton, Colin J. Cotter
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Abstract:Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties.
Comments: Revision to version published on DSCS
Subjects: Numerical Analysis (math.NA); Atmospheric and Oceanic Physics (physics.ao-ph)
Cite as: arXiv:1605.00551 [math.NA]
  (or arXiv:1605.00551v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1605.00551
Journal reference: Dynamics and Statistics of the Climate System, Volume 1, Issue 1, dzw005 (2016)
Related DOI: https://doi.org/10.1093/climsys/dzw005

Submission history

From: Andrea Natale [view email]
[v1] Mon, 2 May 2016 16:33:58 UTC (469 KB)
[v2] Wed, 21 Sep 2016 19:00:40 UTC (471 KB)
[v3] Fri, 13 Oct 2017 23:09:34 UTC (471 KB)
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