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Mixed hp-finite element approximations on geometric edge and boundary layer meshes in three dimensions

by A. Toselli and Ch. Schwab

(Report number 2001-02)

Abstract
In this paper, we consider the Stokes problem in a three-dimensional polyhedral domain discretized with hp finite elements of type Qk for the velocity and Qk-2 for the pressure, defined on hexahedral meshes anisotropically and non quasi-uniformly refined towards faces, edges, and corners. The inf-sup constant of the discretized problem is independent of arbitrarily large aspect ratios and exhibits the same dependence on k as in in the case of isotropically refined meshes. Our work generalizes a recent result for two-dimensional problems in [8,9].

Keywords: Mixed methods, hp finite elements, spectral elements, anisotropic meshes

@Techreport{TS01_279,
  author = {A. Toselli and Ch. Schwab},
  title = {Mixed hp-finite element approximations on geometric edge and boundary layer meshes in three dimensions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2001-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2001/2001-02.pdf },
  year = {2001}
}

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