Toselli, Andrea Neumann-Neumann methods for vector field problems. (English) Zbl 0951.65117 ETNA, Electron. Trans. Numer. Anal. 11, 1-24 (2000). The author introduces and discusses some Schwarz preconditioners for the solution of systems arising from the finite element approximation of some vector field problems (Dirichlet-type boundary value problems). An iterative substructuring method, related to a partition of the original domain into non-overlapping subdomains, is proposed. A hybrid Schwarz preconditioner, called Neumann-Neumann preconditioner, for the Schur complement system corresponding to a variational problem, are built. A logarithmic bound for the condition number of the hybrid Schwarz operator is obtained. Numerical experiments for the hybrid Neumann-Neumann method are presented. Reviewer: Iulian Coroian (Baia Mare) Cited in 6 Documents MSC: 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 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:Schwarz preconditioners; Raviart-Thomas finite elements; domain decomposition; iterative substructuring; Dirichlet-type boundary value problems; Neumann-Neumann preconditioner; Schur complement; condition number; numerical experiments PDFBibTeX XMLCite \textit{A. Toselli}, ETNA, Electron. Trans. Numer. Anal. 11, 1--24 (2000; Zbl 0951.65117) Full Text: EuDML EMIS