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

Heuveline, Vincent; Schieweck, Friedhelm

ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 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.

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