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Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework. (English) Zbl 1065.65136
Summary: FETI-DP preconditioners for two-dimensional elliptic boundary value problems with heterogeneous coefficients are analyzed by the standard additive Schwarz framework. It is shown that the condition number of the preconditioned system for both second-order and fourth-order problems is bounded by \(C(1+\ln (H/h))^2\), where \(H\) is the maximum of the diameters of the subdomains, \(h\) is the mesh size of a quasiuniform triangulation, and the positive constant \(C\) is independent of \(h,H\), the number of subdomains and the coefficients of the boundary value problems on the subdomains. The sharpness of the bound for second-order problems is also established.

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