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

Jesse Chan, Norbert Heuer, Tan Bui-Than, and Leszek F. Demkowicz
Comput. Math. Appl. 67 (4), 771-795, 2014.

We introduce a DPG method for convection-dominated diffusion problems. The choice of test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter [Demkowicz, Heuer: Robust DPG method for convection-dominated diffusion problems, SINUM 51 (5), 2514-2537, 2013]. 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.