We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincaré-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：

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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型不等式时，我们观察到DPG方法的鲁棒性严重不足。我们展示了如何通过使用适当缩放的测试规范来重新建立鲁棒性。作为模型案例，我们研究了泊松问题和Kirchhoff-Love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。对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。