Salt fingering, otherwise known as double diffusion, is an oceanic small-scale phenomenon that has large-scale effects. Double diffusion takes place when warm saline water is present over colder less salty water. Because seawater conducts temperature one hundred times faster than it diffuses salt, the phenomenon of double diffusion occurs. If double diffusion is accurately modeled, then the ocean's temperature and salinity can be analyzed more effectively. This study seeks to use the Galerkin Method to write a mathematical program in order to model oceanic salt fingering. An initial boundary problem is solved in a two-dimensional basin with no bottom topography. The results will be used to analyze the phenomenon of double diffusion, and will provide oceanographers a tool to more effectively analyze the ocean's temperature and salinity properties.