The DPG Method for the Convection-Reaction Problem, Revisited
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin operator - is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.