THE USE OF VARIATIONAL METHODS AND OF ERROR DISTRIBUTION PRINCIPLES IN GROUNDWATER HYDRAULICS

Abstract

The aim of the present paper is to present some mathematical techniques for the solution of problems connected with three-dimensional steady-state groundwater flow with a free surface. The validity of Darcy's law is assumed. As no use is made of the Dupuit-Forschheimer approximation, the shape of the free surface and the velocity potential must be determined simultaneously from a non-linear boundary value problem. In order to demonstrate the use of a variational method and of error distribution principles for the solution of those problems by an example as simple as possible, we investigate the gravity flow of incompressible, homogeneous groundwater towards a circular well completely penetrating an isotropic, homogeneous, inelastic aquifer resting on a horizontal, impermeable substratum.