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Formulation variationnelle et algorithme de décomposition de domaines pour les problèmes elliptiques. (Variational formulation and domain decomposition algorithm for elliptic problems). (French) Zbl 0637.65104
The numerical efficiency of domain decomposition methods is very sensitive to preconditioning. The proposed approach uses the \(H^ 1\) norm on the space of traces of each subdomain. On this space, we invert, by a conjugate gradient method, an operator which involves the solution on each subdomain of a Dirichlet and of a Neumann problem.

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