Exponential convergence in a Galerkin least squares hp-FEM for Stokes flow

A stabilized hp-finite element method (FEM) of Galerkin least squares (GLS) type is analysed for the Stokes equations in polygonal domains. Contrary t o the standard Galerkin FEM, the GLSFEM admits the implementationally attra ctive equal-order interpolation in the velocity and the pressure. In conjun ction with geometrically refined meshes and linearly increasing approximati on orders it is shown that the hp-GLSFEM leads to exponential rates of conv ergence for solutions exhibiting singularities near corners. To obtain this result a novel hp-interpolation result is proved that allows the approxima tion of pressure functions in certain weighted Sobolev spaces in a conformi ng way and at exponential rates of convergence on geometric meshes.