Tracer simulations carried out using the TOUGH2 reservoir simulator are prone to numerical dispersion. This paper describes the development of a separate Lagrange-Galerkin finite-element tracer simulator, used in conjunction with TOUGH2, that introduces minimal numerical dispersion. This approach raises the problem of converting the TOUGH2 flow fields to finite-element format. A new method is presented for carrying out this conversion using a quadratic minimisation technique. Details are given of an initial implementation of the Lagrange-Galerkin method in a tracer simulator, together with example test results to demonstrate its low numerical dispersion. (C) 2004 CNR. Published by Elsevier Ltd. All rights reserved.