On the Inf-sup condition for higher order mixed fem on meshes with hanging nodes

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 Pr-1elements for the pressure where the order r can vary from element to element between 2 and a f1ixed bound r*. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes. © EDP Sciences.