Robustness and Accuracy of Groundwater Flux Computations in Large-Scale Shallow Sedimentary Basins

Abstract

Computer codes to calculate the groundwater potential field ø(x,t) (a scalar field) are applied on a routine basis by geohydrologists. For this purpose both finite difference and finite element codes are well-suited. However, the flux field q(x,t) (a vector field) obtained from the latter finite element codes has discontinuous normal components on the inter-element boundaries. These discontinuities can lead to serious errors in the resulting flow paths. Finite difference codes, on the other hand, result in a continuous flux field. To avoid a discontinuous flux field, while retaining the advantages of the finite element method, the so-called mixed-hybrid finite element method has recently been developed; see Kaasschieter and Huijben [1]. The block-centred finite difference method (see Aziz and Settari [2]) turns out to be a special case of the mixed-hybrid finite element method; or, in other words, the mixed-hybrid finite element method may be considered as a generalization of the blockcentred finite difference method; see Weiser and Wheeler [3].