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Mixed hp-DGFEM for incompressible flows II: Geometric edge meshes

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

(Report number 2002-21)

Abstract
We consider the Stokes problem in three-dimensional polyhedral domains discretized on hexahedral meshes with hp-discontinuous Galerkin finite elements of type IQk for the velocity and IQk-1 for the pressure. We prove that these elements are inf-sup stable on geometric edge meshes that are refined anisotropically and non quasi-uniformly towards edges and corners. The discrete inf-sup constant is shown to be independent of the aspect ratio of the anisotropic elements and is of order {\mathcal O}(k-3/2) in the polynomial degree k, as in the case of IQk-IQk-2 conforming approximations on the same meshes.

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

@Techreport{SST02_307,
  author = {D. Sch\"otzau and Ch. Schwab and A. Toselli},
  title = {Mixed hp-DGFEM for incompressible flows II: Geometric edge meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-21.pdf },
  year = {2002}
}

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