  In this research note we provide a variational basis for the optimal
artificial diffusion method, which has been a cornerstone in developing many
stabilized methods. The optimal artificial diffusion method produces exact
nodal solutions when applied to one-dimensional problems with constant
coefficients and forcing function. We first present a variational principle for
a multi-dimensional advective-diffusive system, and then derive a new stable
weak formulation. When applied to one-dimensional problems with constant
coefficients and forcing function, this resulting weak formulation will be
equivalent to the optimal artificial diffusion method. We present
representative numerical results to corroborate our theoretical findings.
