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

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-field 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.

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