Application of Galerkin's Procedure to aquifer analysis

Abstract

The groundwater flow equations may be solved using the Galerkin procedure to generate the approximating equations. The integrals in the resulting equations may be efficiently evaluated by using isoparametric quadrilateral elements and numerical integration. A comparison of solutions for an idealized problem obtained by using Galerkin techniques and finite difference techniques indicates they achieve approximately the same degree of accuracy. A field application of the two methods shows that the Galerkin procedure provided satisfactory solutions with far fewer nodes than were required for the finite difference approach. In selecting one of the above methods for a particular hydrologic problem the flexibility of the irregular subspaces used in the Galerkin approach must be weighed against the very efficient equation solving schemes applicable to the finite difference equations.