Report 1997-19

Mixed hp Finite Element Methods for Stokes and Non-Newtonian Flow

C. Schwab and M. Suri

Abstract: 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 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.

Keywords: hp finite elements, mixed method, Stokes flow, non-Newtonian flow, EVSS method

Paper: Available as PDF (510 KB) or as hardcopy to order reports@sam.math.ethz.ch.