TY - JOUR
T1 - 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
AU - Wang , Cheng
AU - Sun , Pengtao
JO - Communications in Computational Physics
VL - 1
SP - 124
EP - 143
PY - 2021
DA - 2021/04
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0084
UR - https://global-sci.org/intro/article_detail/cicp/18876.html
KW - Double saddle-point problem, augmented Lagrangian Uzawa method, elliptic interface problem, distributed Lagrange multiplier/fictitious domain (DLM/FD) method.
AB - <p style="text-align: justify;">In this paper, an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite (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.</p>