Mixed hp finite element methods for Stokes and non-Newtonian flow

摘要

We analyze the stability of hp finite elements for viscous incompressible flow. For the classical velocity-pressure formulation, we give new estimates for the discrete inf-sup constants on geometric meshes which are explicit in the polynomial degree k of the elements. In particular, we obtain new bounds for p-elements on triangles. For the three-held Stokes problem describing linearized non-Newtonian flow, we estimate discrete inf-sup constants explicit in both h and k for various subspace choices (continuous and discontinuous) for the extra-stress. We also give a stability analysis of the hp-version of an elastic-viscous-split-stress ( EVSS) method and present elements that are stable and optimal in h and k. Finally, we present numerical results that show the exponential convergence of the hp version for Stokes flow, over unsmooth domains.