Abstract

SummaryIn 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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