o The local discontinuous Galerkin method for contaminant transport

We develop a discontinuous finite element method for advection–diffusion equations arising in contaminant transport problems, based on the Local Discontinuous Galerkin (LDG) method of Cockburn B and Shu CW. (The local discontinuous Garlerkin method for time-dependent convection–diffusion systems. SIAM J Numer Anal 1998;35:2440–63). This method is defined locally over each element, thus allowing for the use of different approximating polynomials in different elements. Furthermore, the elements do not have to conform, or “match-up” at interfaces. The method has a built-in upwinding mechanism for added stability. Moreover, it is conservative. We describe the method for multi-dimensional systems of equations with possibly non-linear adsorption terms, and provide some numerical results in both one and two dimensions. These results examine the accuracy of the method, and its ability to approximate solutions to some linear and non-linear problems arising in contaminant transport.