We discuss two types of discrete inf-sup conditions for the Taylor-Hood family $Q_k$-$Q_{k-1}$ for all $k\in \mathbb{N}$ with $k\ge 2$ in 2D and 3D. While in 2D all results hold for a general class of hexahedral meshes, the results in 3D are restricted to meshes of parallelepipeds. The analysis is based on an element-wise technique as opposed to the widely used macroelement technique. This leads to inf-sup conditions on each element of the subdivision as well as to inf-sup conditions on the whole computational domain.

翻译：我们讨论Taylor-Hood家族的两种互不关联的内衣条件,即2D美元和3D美元,以2D美元和2D美元和2D美元计算,所有美元和1美元。虽然在2D中,所有结果都持有六相色片的一般类别,但3D的结果仅限于平行管道的间衣。分析基于元素智能技术,而不是广泛使用的宏观技术。这导致子系统每个组成部分的内衣条件,以及整个计算域的内衣条件。