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Maximum norm analysis of an overlapping nonmatching grids method for the obstacle problem

Advances in Difference Equations volume 2006, Article number: 085807 (2006) Cite this article

Abstract

We provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from the other subdomain. Under a discrete maximum principle, we show that the discretization on each subdomain converges quasi-optimally in the L∞ norm.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Sultan Qaboos University, P.O. Box 36, Muscat, 123, Oman

    M Boulbrachene

  2. Departement de Mathematiques Faculte des Sciences, Universite Badji Mokhtar, Annaba, BP, 12, Algeria

    S Saadi

Authors
  1. M Boulbrachene
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  2. S Saadi
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Correspondence to M Boulbrachene.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Boulbrachene, M., Saadi, S. Maximum norm analysis of an overlapping nonmatching grids method for the obstacle problem. Adv Differ Equ 2006, 085807 (2006). https://doi.org/10.1155/ADE/2006/85807

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