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Multilevel Schwarz methods. (English) Zbl 0796.65129
The author presents a solution of a system of linear algebraic equations which results from the discretization of second order elliptic equations. A class of multilevel algorithms is studied using the additive Schwarz framework. It is established that the condition number of the iteration operators are bounded independently of the mesh sizes and the number of levels. Numerical experiments are performed for illustration.

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
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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