The convergence of Glowinski's algorithm for elliptic problems (Q1898890)

A theoretical analysis of a non-overlapping domain decomposition algorithm proposed by \textit{J. F. Bourgat, R. Glowinski, P. le Tallec} and \textit{M. Vidrascu} [Proc. 2nd Int. Symp. on Domain Decomposition Methods, Los Angeles/Calif. 1988, 3-16 (1989; Zbl 0684.65094)] is presented. The algorithm can be implemented in parallel, and many numerical experiments have illustrated its efficiency. A proof for the algorithm's convergence and an estimation of the condition number of the preconditioned system can be found in this paper. The authors stop sequentially on the continuous and the discrete case in the two subdomains approach and on the discrete case, in many subdomains approach, and make an analysis of the convergence properties of the algorithm. In the last section an estimation of the condition number of the preconditioned system in the preconditioned conjugate gradient method is given. The theoretical results coincide with the numerical experiments known in advance.