Mixed hp - FEM on anisotropic meshes

Dominik Schötzau, Christoph Schwab, Rolf Stenberg
1997
Mixed hp-FEM for incompressible uid ow 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 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
more » ... 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.
doi:10.3929/ethz-a-004284618 fatcat:z3nfj2jvrjdtvdfsrscx3rfdi4