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On the convergence of a dual-primal substructuring method. (English) Zbl 1003.65126
The authors are concerned with the derivation of polylogarithmic condition number estimates for dual-primal FETI type methods applied to 2nd and 4th order elliptic selfadjoint boundary value problems. It is shown that the condition number of the FETI-DP method with the Dirichlet preconditioner grows like \( O(1+\text{log}(\frac{H}{h}))^{2} \). The result and its proof improve on that given in a previous paper of the authors [Numer. Math. 73, No. 4, 473-487 (1996; Zbl 0880.65087)].

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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