Report 1997-02

Mixed hp-FEM on anisotropic meshes

D. Schoetzau and C. Schwab

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

Paper: Available as PDF (600 KB) or as hardcopy to order reports@sam.math.ethz.ch.