Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?

Abstract

Selected groundwater flow scenarios are used in a two‐way comparison between the mixed hybrid finite element method and the standard finite element method (also called the conforming finite element method). The simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists. The basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element. By contrast, the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential. The conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity. The mixed hybrid finite element method provides velocities everywhere in the field, as well as potentials at the center of each element and each edge. Moreover, the normal component of the velocity field is continuous between adjacent elements. The results of the simulations are presented in the form of streamlines. To avoid the problem of velocity discontinuity, the method of Cordes and Kinzelbach (1992) is used; it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method. The comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy. It is also superior to the conforming method in terms of computational effort. The potential fields obtained by the mixed hybrid and the conforming finite element methods are the same.