Spectral Tau approximation of the two-dimensional stokes problem

Summary We analyse the Spectral Tau method for the approximation of the Stokes system on a square with Dirichlet boundary conditions. We provide an error estimate, in the norm of the Sobolev spaceH ^s, for the approximation of a divergence free vector field with polynomial divergence free vector fields. We apply this result to prove some convergence estimates for the solution of the discrete Stokes problem.This work has been partially supported by the U.S. Army through its European Research Office under contract No. DAJA-84-C 0035