Summary
The Fully Adaptive Multigrid Method (FAMe) is a concept for the effective solution of elliptic problems including robust and efficient iterative solution, error estimation, and self-adaptive refinement. In this paper we introduce a variant of the FAMe similar in structure to a multigrid V-cycle and a multiplicative multilevel Schwarz method. This variant permits a convergence analysis showing that the FAMe provides optimal convergence rates when the classical methods do. The FAMe, however, will be more efficient in a local refinement context by exploiting the locality of the computations and will be more robust, because it naturally provides diagnostic information that can serve as rigorous error bounds.
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© 1994 Springer Fachmedien Wiesbaden
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Rüde, U. (1994). On the V-Cycle of the Fully Adaptive Multigrid Method. In: Hackbusch, W., Wittum, G. (eds) Adaptive Methods — Algorithms, Theory and Applications. Notes on Numerical Fluid Mechanics (NNFM). Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14246-1_17
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DOI: https://doi.org/10.1007/978-3-663-14246-1_17
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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