Analysis of iterative algorithms of Uzawa type for saddle point problems (Q596562)

This paper deals with convergence criteria for iterative algorithms of Uzawa type for solving linear saddle point problems. The eigenvalues of the iteration matrix are studied carefully and some sufficient conditions for convergence are given. The conclusions given here hold for both symmetric and nonsymmetric saddle point problems. These new sufficient conditions are compared with some known results and illustrated by examples. Theoretically these new criteria for convergence are weaker than those given by \textit{J. H. Bramble, J. E. Pasciak}, and \textit{A. T. Vassilev} [Math. Comput. 69, No. 230, 667--689 (2000; Zbl 0951.65122)].