Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, p. 493-505

We consider a family of quadrilateral or hexahedral mixed $hp$-finite elements for an incompressible flow problem 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 an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.

DOI : https://doi.org/10.1051/m2an:2008014
Classification:  65N30,  65N35,  76D07
Keywords: Stokes problem, inf-sup condition, mixed $hp$-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes
@article{M2AN_2008__42_3_493_0,
author = {Schieweck, Friedhelm},
title = {Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
pages = {493-505},
doi = {10.1051/m2an:2008014},
zbl = {1154.76034},
mrnumber = {2423796},
language = {en},
url = {http://www.numdam.org/item/M2AN_2008__42_3_493_0}
}

Schieweck, Friedhelm. Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, pp. 493-505. doi : 10.1051/m2an:2008014. http://www.numdam.org/item/M2AN_2008__42_3_493_0/

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