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Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method

Tsz Shun Eric CHUNG Hyea Hyun Kim Olof B Widlund

TBD mathscidoc:1910.43477

SIAM Journal on Numerical Analysis, 51, (1), 47-67, 2013.1
Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions. The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung and Engquist [<i>SIAM J. Numer. Anal.</i>, 47 (2009), pp. 3820--3848] for the acoustic wave equation. Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on a nonoverlapping subdomain partition, which allows quite general subdomain partitions, and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation. Condition number bounds are established and numerical results are presented.
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@inproceedings{tsz2013two-level,
  title={Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method},
  author={Tsz Shun Eric CHUNG, Hyea Hyun Kim, and Olof B Widlund},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180138202789006},
  booktitle={SIAM Journal on Numerical Analysis},
  volume={51},
  number={1},
  pages={47-67},
  year={2013},
}
Tsz Shun Eric CHUNG, Hyea Hyun Kim, and Olof B Widlund. Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method. 2013. Vol. 51. In SIAM Journal on Numerical Analysis. pp.47-67. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180138202789006.
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