Convergence of a substructuring method with Lagrange multipliers

We analyze the convergence of a substructuring iterative method with Lagrange multipliers, proposed recently by Farhat and Roux. 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, we prove the asymptotic bound on the condition number C(1+log(H/h))(gamma), gamma = 2 or 3, where h is the characteristic element size and H subdomain size.