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Mixed hp-DGFEM for incompressible flows III: Pressure stabilization

by D. Schötzau and Ch. Schwab and A. Toselli

(Report number 2002-25)

Abstract
We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that IQk-IQk and IQk-IQk-1 elements satisfy a generalized inf-sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, edges, and corners. The discrete inf-sup constant is proven to be independent of the aspect ratios of the anisotropic elements and to decrease as k-1/2 with the approximation order. We also show that the generalized inf-sup condition leads to a global stability result in a suitable energy norm.

Keywords: hp-FEM, discontinuous Galerkin methods, Stokes problem, anisotropic refinement

@Techreport{SST02_311,
  author = {D. Sch\"otzau and Ch. Schwab and A. Toselli},
  title = {Mixed hp-DGFEM for incompressible flows III: Pressure stabilization},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-25.pdf },
  year = {2002}
}

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