An Augmented Lagrangian Uzawa Iterative Method for Solving Double Saddle-Point Systems with Semidefinite (2,2) Block and its Application to DLM/FD Method for Elliptic Interface Problems

In this paper, an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semi definite (2,2) block. Convergence of the iterative method is proved under the assumption that the double saddle-point problem exists a unique solution. An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain (DLM/FD) finite element method for solving elliptic interface problems is also presented, in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method. Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.