Finite elements and characteristics applied to advection-diffusion equations

This paper deals with an algorithm for the solution of advection-diffusion equations based on the finite element method combined with the discretization of the total differential D rho/Dt. The finite difference analog of the Galerkin method is given in the one-dimensional case. Diffusion of the scheme is studied in the two-dimensional case by means of a classic example. It is shown that the scheme is stable, has no phase error and leads to simple problems at each time step.