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We propose an inexact Uzawa algorithm with two variable relaxation parametersfor solving the generalized saddle-point system. The saddle-point problems canbe found in a wide class of applications, such as the augmented Lagrangianformulation of the constrained minimization, the mixed finite element method,the mortar domain decomposition method and the discretization of elliptic andparabolic interface problems. The two variable parameters can be updated ateach iteration, requiring no a priori estimates on the spectrum of twopreconditioned subsystems involved. The convergence and convergence rate of thealgorithm are analysed. Both symmetric and nonsymmetric saddle-point systemsare discussed, and numerical experiments are presented to demonstrate therobustness and effectiveness of the algorithm.

An Inexact Uzawa Algorithm for Generalized Saddle-Point Problems and Its Convergence