An adjoint Petrov - Galerkin method was proposed by Neuman [1] to solve multidimensional advection - dispersion equation. The method uses a numerical solution of the adjoint state equation on a sequence of nested grids to compute the weight functions. A numerical application of the method shows that at low Peelet numbers, the application of method results in a satisfactory match between the analytical and the numerical solutions. When the Peelet number increases and advection become dominant, the results obtained show oscillations of the concentration profile and a lag between the analytical and the numerical solution. The oscillations are a function of the Peelet and Courant numbers. Accurate solutions are obtained when the Courant number is
equal to one, for Peelet number up to 50. For Peelet number greater than 50, the numerical solution lags behind the analytical solution. At other Courant numbers, the maximum Peelet number for stable solution drops off rapidly.
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