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On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes

Published online by Cambridge University Press:  26 April 2007

Vincent Heuveline  and
Friedhelm Schieweck
Vincent Heuveline
Affiliation:
Institute for Applied Mathematics II, University Karlsruhe (TH), Postfach 6980, 76128 Karlsruhe, Germany. vincent.heuveline@math.uni-karlsruhe.de Scientific Supercomputing Center, University of Karlsruhe (TH), Zirkel 2, 76128 Karlsruhe, Germany. vincent.heuveline@rz.uni-karlsruhe.de
Friedhelm Schieweck
Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany. friedhelm.schieweck@mathematik.uni-magdeburg.de
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Abstract

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-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.

Keywords

Inf-sup conditionhigher order mixed finite elementadaptive gridshanging nodes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 1 , January 2007 , pp. 1 - 20
Copyright
© EDP Sciences, SMAI, 2007

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