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Convergence of a substructuring method with Lagrange multipliers. (English) Zbl 0880.65087
The convergence of a substructuring iterative method with Lagrange multipliers is analyzed. This method was recently proposed by C. Farhat and 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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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