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Uniformly stable mixed hp-finite elementson multilevel adaptive grids with hanging nodes

Published online by Cambridge University Press:  03 April 2008

Friedhelm Schieweck
Friedhelm Schieweck*
Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany. [email protected]
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Abstract

We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Q r -elements for the velocity anddiscontinuous $P_{r-1}$ -elements for the pressure where the orderr can vary from element to elementbetween 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 meshsize and the polynomial degree.

Keywords

Stokes probleminf-sup conditionmixed hp-FEMquadrilateral and hexahedral finite elementsmultilevel adaptive gridshanging nodes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 3 , May 2008 , pp. 493 - 505
Copyright
© EDP Sciences, SMAI, 2008

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