MIXED HP-FEM ON ANISOTROPIC MESHES

Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are a nalyzed. A discrete inf-sup condition is proved with a constant indepe ndent of the meshwidth and the aspect ratio. For each polynomial degre e k greater than or equal to 2 we present velocity-pressure subspace p airs which are stable on quadrilateral mesh-patches independently of t he element aspect ratio, implying in particular divergence stability o n the so-called Shishkin-meshes. Moreover, the inf-sup constant is sho wn to depend on the spectral order k like k(-1/2) for quadrilateral me shes and like k(-3) for meshes containing triangles. New consistency r esults for spectral elements on anisotropic meshes are also proved.