Hybrid Laplace transform ®nite element method for solving the convection±dispersion problem

It can be very time consuming to use the conventional numerical methods, such as the ®nite element method, to solve convection± dispersion equations, especially for solutions of large-scale, long-term solute transport in porous media. In addition, the conventional methods are subject to arti®cial di€usion and oscillation when used to solve convection-dominant solute transport problems. In this paper, a hybrid method of Laplace transform and ®nite element method is developed to solve oneand two-dimensional convection±dispersion equations. The method is semi-analytical in time through Laplace transform. Then the transformed partial di€erential equations are solved numerically in the Laplace domain using the ®nite element method. Finally the nodal concentration values are obtained through a numerical inversion of the ®nite element solution, using a highly accurate inversion algorithm. The proposed method eliminates time steps in the computation and allows using relatively large grid sizes, which increases computation eciency dramatically. Numerical results of several examples show that the hybrid method is of high eciency and accuracy, and capable of eliminating numerical di€usion and oscillation e€ectively. Ó 1999 Elsevier Science Ltd. All rights reserved.