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

by Ch. Schwab and M. Suri

(Report number 1997-19)

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

@Techreport{SS97_224,
  author = {Ch. Schwab and M. Suri},
  title = {Mixed hp Finite Element Methods for Stokes and Non-Newtonian Flow},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1997-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1997/1997-19.pdf },
  year = {1997}
}

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