  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.
