A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms

We introduce a DPG method for convection-dominated diffusion problems. The choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter (Demkowicz and Heuer 2011)  [18]. We propose a new inflow boundary condition which regularizes the adjoint problem, allowing the use of a stronger test norm. The robustness of the method is proven, and numerical experiments demonstrate the method’s robust behavior.