MIXED hp-FEM ON ANISOTROPIC MESHES

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≥2 we present velocity-pressure subspace pairs 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.