Iterative solution techniques for the stokes and Navier‐Stokes equations

The linear system arising from a Lagrange‐Galerkin mixed finite element approximation of the Navier–Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one‐level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two‐level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.