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A relaxation procedure for domain decomposition methods using finite elements. (English) Zbl 0661.65111
We present the convergence analysis of a new domain decomposition technique for finite element approximations. This technique is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly it is adjacent. No global preconditioner is needed in the practice, but simply single-domain solvers, reducing at most the computational complexity. An optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated. Applications are given to elliptic equations and to incompressible Stokes equations.
Reviewer: L.D.Marini

MSC:
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
76D07 Stokes and related (Oseen, etc.) flows
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