The convergence factor of preconditioned algorithms of the Arrow-Hurwicz type. (English) Zbl 0674.65008
The preconditioned Arrow-Hurwicz-algorithm to solve the linear system \(Au+Bp=f\), \(B^ Tu=g\) is a modification of Uzawa’s algorithm, which was studied earlier by the author and U. Langer [J. Comput. Appl. Math. 15, 191-202 (1986; Zbl 0601.76021)]. The iteration parameters are chosen optimally. The convergence factor is estimated, in particular it is independent of the discretization parameter, if the system in question stems from certain mixed finite element problems. Some computational aspects are discussed. Finally, a general method to construct the preconditioning operators is given.
Reviewer: L.Berg
MSC:
65F10 | Iterative numerical methods for linear systems |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65F35 | Numerical computation of matrix norms, conditioning, scaling |
35J25 | Boundary value problems for second-order elliptic equations |
35J40 | Boundary value problems for higher-order elliptic equations |