Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes

摘要

We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Q(r)-elements for the velocity and discontinuous Pr-1-elements for the pressure where the order r can vary from element to element between 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 mesh size and the polynomial degree.