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

A stabilized hp-finite element method (FEM) of Galerkin leastsquares (GLS) type is analysed for the Stokes equations in polygonaldomains. Contrary to the standard Galerkin FEM, the GLSFEM admitsthe implementationally attractive equal-order interpolationin the velocity and the pressure. In conjunction with geometricallyrefined meshes and linearly increasing approximation ordersit is shown that the hp-GLSFEM leads to exponential rates ofconvergence for solutions exhibiting singularities near corners.To obtain this result a novel hp-interpolation result is provedthat allows the approximation of pressure functions in certainweighted Sobolev spaces in a conforming way and at exponentialrates of convergence on geometric meshes. Received 6 June 1999. Accepted 14 March 2000.