An new improved Uzawa method for finite element solution of Stokes problem

Abstract

 Tchebychev iteration may be used for acceleration convergence of an iterative algorithm to solve a general linear system equation. Associating it with the Uzawa method, we suggest a new iterative solution method for the Stokes problems. The new algorithm retains the simplicity and robustness of the Uzawa method. So it requires almost no additional cost of computation, in terms of storage or CPU time, yet it provides the property of speed up convergence. Numerical tests showed that the algorithm of this type have much faster convergence rates than both the original Uzawa iterative algorithm and the augmented Lagrangian method.