A Multilevel Algorithm for Mixed Problems

We describe a multilevel algorithm for the numerical solution of symmetric indefinite problems which arise, e.g. from mixed finite element approximations of the Stokes equation. The main difficulty, besides the indefiniteness, is the lack of regularity of the solution of the corresponding continuous problem. This is overcome by introducing a scale of mesh-dependent norms. The convergence rate of the described algorithm is bounded independently of the meshsize. For convenience we only discuss Jacobi relaxation as smoothing operator in detail. In the last section we comment on Lanczos-type smoothing procedures.