In this work we consider the
dual-primal Discontinuous Petrov–Galerkin (DPG)
method for the advection-diffusion model problem.
Since in the DPG method both
mixed internal variables are discontinuous,
a static condensation procedure can be
carried out, leading to a single-field nonconforming
discretization scheme. For this latter formulation,
we propose a flux-upwind stabilization technique to deal with
the advection-dominated case.
The resulting scheme is conservative and satisfies a discrete
maximum principle under standard geometrical assumptions on
the computational grid. A convergence analysis is
developed, proving first-order accuracy of the
method in a discrete H1-norm, and the numerical performance
of the scheme is validated on benchmark problems with
sharp internal and boundary layers.