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The Galerkin method of approximation in conjunction with the finite element method of analysis may be used to simulate the movement of groundwater contaminants. In solving the groundwater flow and mass transport equations this approach allows a functional representation of the dispersion tensor, transmissivity tensor, and fluid velocity, as well as an accurate representation of boundaries of irregular geometry. A field application of the method to chromium contamination on Long Island, New York, shows that accurate simulations can be obtained by using the Galerkin-finite element approach.