Convergence of a substructuring method with Lagrange multipliers
The convergence of a substructuring iterative method with Lagrange multipliers is analyzed. This method was recently proposed by \textit{C. Farhat} and \textit{F.-X. Roux} [Int. J. Numer. Methods Eng. 32, No. 6, 1205-1227 (1991; Zbl 0758.65075)]. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, an asymptotic bound on the condition number is derived.
scientific article; zbMATH DE number 932025