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Mixed hp-FEM on anisotropic meshes

by D. Schoetzau and Ch. Schwab

(Report number 1997-02)

Abstract
Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf-sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree $k\geq 2$, velocity-pressure subspace pairs are presented which are stable on quadrilateral mesh-patches, independently of the element aspect ratio implying in particular divergence stability on the so-called Shishkin-meshes. Moreover, the inf-sup constant is shown to depend on the spectral order k like $k^{-1/2}$ for quadrilateral meshes and like $k^{-3}$ for meshes containing triangles. New consistency results for spectral elements on anisotropic meshes are also proved.

Keywords: hp-Finite Elements, Spectral Elements, Mixed FEM, anisotropic meshes

@Techreport{SS97_207,
  author = {D. Schoetzau and Ch. Schwab},
  title = {Mixed hp-FEM on anisotropic meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1997-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1997/1997-02.pdf },
  year = {1997}
}

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