Chan, Tony F.; Hou, Thomas Y.; Lions, P. L. Geometry related convergence results for domain decomposition algorithms. (English) Zbl 0724.65109 SIAM J. Numer. Anal. 28, No. 2, 378-391 (1991). 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. Reviewer: T.Sonar (Stuttgart) Cited in 1 ReviewCited in 16 Documents 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 Keywords:convergence; domain decomposition; Schwarz alternating procedure; Schwarz algorithm; preconditioner; nonoverlapping Schur complement algorithms; condition number; T-shaped domains PDFBibTeX XMLCite \textit{T. F. Chan} et al., SIAM J. Numer. Anal. 28, No. 2, 378--391 (1991; Zbl 0724.65109) Full Text: DOI