Uzawa-Low method and preconditioned Uzawa-Low method for three-order block saddle point problem

In this paper, Uzawa-Low method for three-order block saddle point problem is presented and the corresponding convergence conditions are established. Furthermore, by introducing a preconditioner, we propose centered preconditioned Uzawa-Low method (CPU-Low method) and obtain its convergence conditions as well. Experimental results show that the two proposed methods are more efficient than Uzawa-Low method for the original saddle point problem and the CPU-Low method is superior to the Uzawa-Low method for three-order block saddle point problem.