Compatible finite element spaces for geophysical fluid dynamics
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Dynamics and Statistics of the Climate System, (November 2016)

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 non-linear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarize 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.
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