On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 1, p. 1-20

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with ${Q}_{r}$-elements for the velocity and discontinuous ${P}_{r-1}$-elements for the pressure where the order $r$ can vary from element to element between $2$ and a fixed bound ${r}^{*}$. We prove the inf-sup condition uniformly with respect to the meshwidth $h$ on general quadrilateral and hexahedral meshes with hanging nodes.

DOI : https://doi.org/10.1051/m2an:2007005
Classification:  65N30,  65N35
Keywords: inf-sup condition, higher order mixed finite element, adaptive grids, hanging nodes
@article{M2AN_2007__41_1_1_0,
author = {Heuveline, Vincent and Schieweck, Friedhelm},
title = {On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
pages = {1-20},
doi = {10.1051/m2an:2007005},
zbl = {1129.65086},
mrnumber = {2323688},
language = {en},
url = {http://www.numdam.org/item/M2AN_2007__41_1_1_0}
}

Heuveline, Vincent; Schieweck, Friedhelm. On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 1, pp. 1-20. doi : 10.1051/m2an:2007005. http://www.numdam.org/item/M2AN_2007__41_1_1_0/

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