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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 -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.

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