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Analysis of multilevel decomposition iterative methods for mixed finite element methods. (English) Zbl 0823.65035
Multilevel extensions of the two-level Schwarz algorithm [see R. E. Ewing and J. Wang, ibid. 26, No. 6, 739-756 (1992; Zbl 0765.65104)] are considered for second-order elliptic equations. The authors show that, without any regularity assumptions, the algorithms converge with rate bounded by \(1 - w(2-w)/ (CJ)\) for some constant \(C\) where \(J\) is the number of levels and \(0 < w < 2\) is a relaxation parameter. Furthermore, if the full \(H^ 2\) regularity is satisfied for the operator \(- \nabla \cdot (c\nabla)\) with homogeneous Dirichlet boundary condition, then uniform convergence is possible. Numerical results are presented to illustrate the efficiency of the proposed algorithms.
Reviewer: L.S.Ioffe (Haifa)

MSC:
65F10 Iterative numerical methods for linear systems
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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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