The convergence rate of the minimal residual method for the Stokes problem

Summary.

Discretisation of the classical Stokes problem gives rise to symmetric indefinite matrices with eigenvalues which, in a precise way, are not symmetric about the origin, but which do depend on a mesh size parameter. Convergence estimates for the Conjugate Residual or Minimum Residual iterative solution of such systems are given by best minimax polynomial approximations on an inclusion set for the eigenvalues. In this paper, an analytic convergence estimate for such problems is given in terms of an asymptotically small mesh size parameter.