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arXiv · 2205.14223

A short note on inf-sup conditions for the Taylor-Hood family $Q_k$-$Q_{k-1}$

Walter Zulehner
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Abstract

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.

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Walter Zulehner. 2024-04-19. A short note on inf-sup conditions for the Taylor-Hood family $Q_k$-$Q_{k-1}$. https://arxiv.org/abs/2205.14223

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