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Fictitious components and subdomain alternating methods. (English) Zbl 0816.65094

Summary: The paper describes one of the versions of the method of fictitious components for elliptic boundary value problems in the generalized formulation. Conditions are defined for the convergence of the method constructed, and convergence rate estimates are given. The Schwarz subdomain alternating method which is dual with respect to the method of fictitious components is also considered, and conditions for its convergence are formulated. The paper ends with illustrating the convergence rate for the methods proposed in the one-dimensional case.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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