STABILITY AND CONVERGENCE OF A FINITE ELEMENT METHOD FOR REACTIVE TRANSPORT IN GROUND WATER

摘要

An explicit finite element method is used to solve the linear convection-diffusion reaction equations governing contaminant transport in ground water flowing through an adsorbing porous medium. The use of discontinuous finite elements for the convective part of the equations combined with mixed finite elements for the diffusive part renders the method for the concentration solution, which displays strong gradients, trivially conservative and fully parallelizable. We carry out a stability and convergence analysis. In particular, the method is proven to satisfy a maximum principle, to be total variation bounded, and to converge to the unique weak solution of the equations. Special attention is paid to the convective part of the equations. Numerical simulations are presented and discussed. [References: 22]