The Convergence Factor of Preconditioned Algorithms of the Arrow–Hurwicz Type

The convergence properties of the Arrow–Hurwicz algorithm for solving mixed finite-element problems are studied. Using a purely algebraic technique, the convergence factor of the algorithm will be estimated. The iteration parameters depending on the smallest and greatest eigenvalues of some generalized eigenvalue problems can be chosen optimally. For special cases, the convergence factor of the preconditioned Arrow–Hurwicz Algorithm is independent of the discretization parameter. Finally, a quite general method that allows us to construct preconditioning operators of the Arrow–Hurwicz Algorithm for a wide class of problems is presented.