Convergence estimates for multigrid algorithms without regularity assumptions

@article{Bramble1991ConvergenceEF,
  title={Convergence estimates for multigrid algorithms without regularity assumptions},
  author={James H. Bramble and Joseph E. Pasciak and Jun Ping Wang and Jinchao Xu},
  journal={Mathematics of Computation},
  year={1991},
  volume={57},
  pages={23-45}
}
A new technique for proving rate of convergence estimates of multi- grid algorithms for symmetric positive definite problems will be given in this paper. The standard multigrid theory requires a "regularity and approxima- tion" assumption. In contrast, the new theory requires only an easily verified approximation assumption. This leads to convergence results for multigrid re- finement applications, problems with irregular coefficients, and problems whose coefficients have large jumps. In… 

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