## 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

Zbl 0765.65104
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### References:

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