  The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and
experimentally positive. We present the method and prove convergence and
$L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical
finite element setting (FEM), the method is compared to Primal
Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual
Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is
difficult to implement numerically but, in the numerical context of this note,
it is far superior to all others.
