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Volume 3, Issue 4
Multigrid and MGR[$v$] Methods for Diffusion Equations

Seymour V. Parter & David Kamowitz

J. Comp. Math., 3 (1985), pp. 373-384.

Published online: 1985-03

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  • Abstract

The MGR[$v$] Algorithm of Ries, Trottenberg and Winter with v=0 and the Algorithm 2.1 of Braess are essentially the same multigrid algorithm for the discrete poisson equation. In this report we consider the extension to the general diffusion equation. In particular, we indicate the proof of the basic result $ρ≤\frac{1}{2}(1+Kh)$, thus extending the results of Braess and Ries Trottenberg and Winter. In addition to this theoretical result we present computational results which indicate that other constant coefficient estimates carry over to this case.

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@Article{JCM-3-373, author = {Seymour V. Parter and David Kamowitz}, title = {Multigrid and MGR[$v$] Methods for Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {4}, pages = {373--384}, abstract = {

The MGR[$v$] Algorithm of Ries, Trottenberg and Winter with v=0 and the Algorithm 2.1 of Braess are essentially the same multigrid algorithm for the discrete poisson equation. In this report we consider the extension to the general diffusion equation. In particular, we indicate the proof of the basic result $ρ≤\frac{1}{2}(1+Kh)$, thus extending the results of Braess and Ries Trottenberg and Winter. In addition to this theoretical result we present computational results which indicate that other constant coefficient estimates carry over to this case.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9633.html} }
TY - JOUR T1 - Multigrid and MGR[$v$] Methods for Diffusion Equations AU - Seymour V. Parter & David Kamowitz JO - Journal of Computational Mathematics VL - 4 SP - 373 EP - 384 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9633.html KW - AB -

The MGR[$v$] Algorithm of Ries, Trottenberg and Winter with v=0 and the Algorithm 2.1 of Braess are essentially the same multigrid algorithm for the discrete poisson equation. In this report we consider the extension to the general diffusion equation. In particular, we indicate the proof of the basic result $ρ≤\frac{1}{2}(1+Kh)$, thus extending the results of Braess and Ries Trottenberg and Winter. In addition to this theoretical result we present computational results which indicate that other constant coefficient estimates carry over to this case.

Seymour V. Parter and David Kamowitz. (1985). Multigrid and MGR[$v$] Methods for Diffusion Equations. Journal of Computational Mathematics. 3 (4). 373-384. doi:
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