In this work we describe and test the construction of least squares Whitney forms based on weights. If, on the one hand, the relevance of such a family of differential forms is nowadays clear in numerical analysis, on the other hand the selection of performing sets of supports (hence of weights) for projecting onto high order Whitney forms turns often to be a rough task. As an account of this, it is worth mentioning that Runge-like phenomena have been observed but still not resolved completely. We hence move away from sharp results on unisolvence and consider a least squares approach, obtaining results that are consistent with the nodal literature and making some steps towards the resolution of the aforementioned Runge phenomenon for high order Whitney forms.

翻译：本文描述并测试了基于权重的加权最小二乘Whitney形式的构造方法。一方面，这类微分形式族在数值分析中的重要性现已明确；另一方面，为高阶Whitney形式投影选择有效的支撑集（即权重）至今仍是一项困难任务。值得注意的是，Runge现象虽已被观测到，但尚未得到完全解决。因此，我们放弃对唯一可解性的严格追求，转而采用最小二乘方法，获得了与节点型文献一致的结果，并为解决高阶Whitney形式中前述Runge现象迈出了若干步骤。