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quadrilateral and hexahedral finite elements

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Uniformly stable mixed hp-finite elementson multilevel adaptive grids with hanging nodes
Friedhelm Schieweck
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 42 / Issue 3 / May 2008

Published online by Cambridge University Press:

03 April 2008, pp. 493-505

Print publication:

May 2008
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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.