Robust DPG method for convection-dominated diffusion problems
Leszek F. Demkowicz and Norbert Heuer
SIAM J. Numer. Anal. 51 (5), 2514-2537, 2013.
We propose and analyze a DPG method for convection-dominated
diffusion problems which provides robust L2 error estimates
for the field variables, and which are quasi-optimal in the energy norm.
Key feature of the method is to construct test functions defined
by a variational formulation with bilinear form (test norm)
specifically designed for the goal of robustness.
Main theoretical ingredient is a stability analysis of the adjoint problem.
Numerical experiments underline our theoretical results and, in
particular, confirm robustness of the DPG method for well-chosen test norms.