On the convergence factor of Uzawa's algorithm

摘要

In this paper we study convergence properties of Uzawa-type algorithms for the iterative solution of mixed finite element approximations to two-dimensional boundary value problems with equality constraints, such as the plane Stokes problem or the plane incompressible elasticity problem. We present estimates of the convergence factors which are optimal with respect to the discretization parameter h. It is shown, in particular, that for the problems mentioned the convergence factor of the classical Uzawa-algorithm is independent of h.