J. Comp. Math., 3 (1985), pp. 373-384. Multigrid And MGR[nu] Methods For Diffusion Equations Seymour V. Parter 1, David Kamowitz 11 University of Wisconsin-Madison Abstract The MGR[v] algorithm of Ries, Trottenberg and Winter with v=0 and the algorith 2.1 of Braess are essentially the same multigrid algorithm for the discrete posion equation. In this report we consider the extension to the general diffusion equation. In particular, we indicate the proof of the basic result $\ru \leq 1/2(1+Kh)$, thus extending the results of Braess and Ries...,In addition to this theoretical result we present computational results which indicate that other constant coefficient estimates carry over this case. Key words: