The physical problem dealt with in this article is the unsteady groundwater flow in an isotropic, nonhomogenous aquifer of limited horizontal extent and arbitrary boundary shape.

The unsteady ground-water level is described by a differential equation which is solved by the Galerkin finite element method, combined with orthogonal eigenfunctions. Unlike many numerical procedures the physical properties of the aquifer are not lost. Boundary conditions are provided by nature in the form of watertight rocks, rivers, lakes or any kind of constant water level in hydraulic contact with the aquifer, or given boundary inflow or outflow.