A consistent finite element material balance is developed for the two dimensional convection-diffusion equation. The resulting numerical scheme is an average of the conventional Galerkin procedure for both the divergence and nondivergence form of the continuity equations. This derivation is valid for finite dimensional approximating spaces having the property that the basis functions sum to unity. Computational molecules are associated with each basis function of the finite dimensional approximating space. The physical significance of coefficients appearing in the resulting material balance governing every computational molecule is discussed. The scheme is compared with standard finite difference procedures. Regularization of the resulting numerical scheme is accomplished by lumping and upstream weighting.