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.

中文翻译：

---

强大的DPG大域方法

当在大域上求解问题并且稳定性基于庞加莱e型不等式时，我们观察到DPG方法的强大不足。我们展示了如何通过使用适当缩放的测试规范来重建鲁棒性。作为模型案例，我们研究了泊松问题和基尔霍夫-洛夫板弯曲模型，还包括了完全离散的变体，其中逼近了最佳测试函数。这两个模型问题的数值实验，包括各向同性域和混合边界条件，证实了我们的发现。