Dryja, Maksymilian; Smith, Barry F.; Widlund, Olof B. Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. (English) Zbl 0818.65114 SIAM J. Numer. Anal. 31, No. 6, 1662-1694 (1994). This interesting paper is devoted to the construction of efficient preconditioners for discretized second-order elliptic problems with symmetric and positive definite operators. Spectrally equivalent or nearly spectrally equivalent model operators are obtained due to a proper splitting of the finite element subspace and the corresponding additive splitting of the inverse operator. Special attention is paid to estimates independent of large variations in the coefficients.The authors provide a review of recent work in substructuring algorithms (about 70 references are given). It seems to me that connections with some earlier papers and especially that of A. M. Ostrowskii (1963) should be mentioned because “Additive Schwarz Methods” on algebraic level is closely connected with multisplitting algorithms for linear systems. Reviewer: E.D’yakonov (Moskva) Cited in 70 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:additive Schwarz methods; preconditioners; second-order elliptic problems; splitting; finite element; substructuring algorithms × Cite Format Result Cite Review PDF Full Text: DOI