Discontinuous Galerkin (DG) methods constitute a promising and relatively new class of methods for computing numerical solutions of partial differential equations. In a simple setting related to multi-layer modeling of ocean circulation, an analysis shows that DG methods are highly accurate in simulating the propagation of inertia-gravity waves. This result suggests that DG methods may give accurate simulations of geostrophic adjustment, an important mechanism in the evolution of geophysical fluid flows. This talk will include overviews of DG methods and the process of geostrophic adjustment, a derivation of an analytical test problem, and some numerical results. The test problem involves wave propagation, multiple time scales, a Riemann problem, the Coriolis effect, and the conservation of potential vorticity.