A robust DPG method for large domains

Abstract: We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincar\'e-type inequality. We show how robustness can be re-established by using appropriately scaled test norms. As model cases we study the Poisson problem and the Kirchhoff--Love plate bending model, and also include fully discrete variants where optimal test functions are approximated. Numerical experiments for both model problems, including an-isotropic domains and mixed boundary conditions, confirm our findings.