Summary
In this paper we discuss convergence of multigrid methods with respect to the maximum norm for 2D elliptic boundary value problems. Our analysis uses Hackbusch’s framework based on the Smoothing Property and Approximation Property (cf. [4]). We present a rather general framework for establishing the Smoothing Property in the maximum norm. The analysis fits in nicely with the classical theory of diagonally dominant matrices and of M-matrices.
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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Reusken, A. (1993). The Smoothing Property for Regular Splittings. In: Hackbusch, W., Wittum, G. (eds) Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85732-3_14
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DOI: https://doi.org/10.1007/978-3-322-85732-3_14
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07641-2
Online ISBN: 978-3-322-85732-3
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