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On the convergence of spectral multigrid methods for solving periodic problems. (English) Zbl 0772.65078

The author considers the numerical solution of elliptic partial differential equations with periodic boundary conditions by methods that are based on a combination of collocation-spectral methods and multigrid methods. Using a unified approach based on variational formulation, the author proves the optimal rate of convergence for several variants of spectral multigrid methods proposed earlier, namely the one based on the nonnested discretization, the filtered one and the midpoint- discretization one. The performance of the methods is compared by means of numerical experiments.
Reviewer: Z.Dostal (Ostrava)

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N35 Spectral, collocation and related 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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