Postprint version. Published in Water Resources Research, Volume 21, Issue 9, September 1, 1985, pages 1354-1360. An edited version of this paper was published by AGU. Copyright 1985 American Geophysical Union. To view the published open abstract, go to http://dx.doi.org/10.1029/WR021i009p01354.
A new numerical method called the finite analytic (FA) method is used to solve a groundwater solute transport problem. The basic idea of the finite analytic method is the incorporation of local analytic solution in the numerical solution of the partial differential equation. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in an element and its neighboring nodal points. The assemble of the linear system equations results in a tridiagonal matrix. Like most finite difference method, the advantages of using efficient iterative techniques for solving tridiagonal matrices are equally applicable to FA method. The automatic localized upstream shift and the analytic property of the FA method eliminates the difficulty of numerical dispersion locally and suppresses the overall numerical dispersion for large Peclet number. For small Peclet number FA method yields excellent results in comparison with the analytic solution. For large Peclet number FA solutions are oscillation free with some degree of numerical dispersion. The results are comparable with those obtained using upstream weighted finite element method.