A short note on inf-sup conditions for the Taylor-Hood family Q_k-Q_k-1

05/27/2022

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by   Walter Zulehner, et al.

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We discuss two types of discrete inf-sup conditions for the Taylor-Hood family Q_k-Q_k-1 for all k∈ℕ with k≥ 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.