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The Australian Journal of Mathematical Analysis and Applications, Volume 7, Issue 2, Article 27, pp. 1-6, 2011, presents a study on the uniform convergence of the Schwarz method for noncoercive variational inequalities. The authors, M. HAIOUR and E. HADIDI, provide a simple proof for the main result concerning L∞ error estimates using the Zhou geometrical convergence and the L∞ approximation given for finite element methods by Courty-Dumont. The paper focuses on noncoercive variational inequalities, using the Schwarz method, which involves decomposing the domain into two subdomains. The authors establish the existence and uniqueness of the solution, introduce the continuous Schwarz method, and consider the discrete problem, providing a survey similar to the one in the continuous case. The discrete Schwarz method is given, and the authors prove the existence of a constant C independent of h, such that the L∞ error estimate is bounded by Ch2 |ln h|2. The paper concludes with a proof of the main result, Theorem 4.1, which states that there exists a constant C independent of h, such that the L∞ error estimate is bounded by Ch2 |ln h|2.

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The Australian Journal of Mathematical Analysis and Applications, Volume 7, Issue 2, Article 27, pp.

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  • File Format: PDF
  • File Size: 116 KB
  • Pages: 6
  • Language: EN
  • Total Downloads: 150
  • Last Updated: 3 hours ago

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