Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities

@article{Badea2003ConvergenceRA,
  title={Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities},
  author={Lori Badea and Xuecheng Tai and Junping Wang},
  journal={SIAM J. Numer. Anal.},
  year={2003},
  volume={41},
  pages={1052-1073}
}
This paper derives a linear convergence for the Schwarz overlapping domain decomposition method when applied to constrained minimization problems. The convergence analysis is based on a minimization approach to the corresponding functional over a convex set. A general framework of convergence is established for some multiplicative Schwarz algorithm. The abstract theory is particularly applied to some obstacle problems, which yields a linear convergence for the corresponding Schwarz overlapping… 

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