Overview of the Finite Element Method in Groundwater Hydrology

Abstract

Since its introduction into the groundwater literature during the mid 1960’s, the finite element method has developed into a very powerful numerical tool for analyzing a variety of groundwater flow problems. Applications of the method cover flow in multi-aquifer systems, flow with a free surface, saturated-unsaturated flow, land subsidence, fractured-porous systems, and large groundwater basins under steady or nonsteady conditions. The method derives its power from the fact that it uses a very general technique for the evaluation of spatial gradients in any direction at any point within the flow domain. This advantage is complemented in the method by an integral statement of the conservation equation at the point of interest. The algorithms stemming from this approach permit relatively simple geometric inputs, even when the problem of interest has complex geometries. From a conceptual perspective there is reason to suspect that alternate formulations of the finite element method may be possible in which the weighted integration technique is dispensed with in favor of an explicit definition of the subdomains of integration. The flexibility of existing finite element algorithms may be enhanced by having options for inputting preprocessed geometric inputs in addition to nodal point coordinates and element lists. Direct formulation of the finite element equations from conservation integrals may provide an alternative that deserves attention. With the advent of mini computers, the finite element method promises to become an every day tool for the practising engineer during the 1980’s.