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Geometry related convergence results for domain decomposition algorithms. (English) Zbl 0724.65109

The authors prove that the Schwarz alternating procedure for general second-order elliptic partial differential equations converges at a rate independent of the aspect ratio for L-, T- and C-shaped domains. Continuous as well as discrete versions of the Schwarz algorithm are covered by these results. Using a certain preconditioner the results presented also apply to the nonoverlapping Schur complement algorithms. It is shown that the condition number of the preconditioned interface operator is bounded by 2 for all L- and T-shaped domains.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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