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FETI-DP preconditioners for a staggered discontinuous Galerkin formulation of the two-dimensional Stokes problem

Hyea Hyun Kim Tsz Shun Eric CHUNG Chak Shing Lee

TBD mathscidoc:1910.43519

Computers & Mathematics with Applications, 68, (12), 2233-2250, 2014.12
In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C (H/h) and C (1+ log (H/h)) 2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant C depending on the infsup constant of the discrete spaces but independent of any mesh parameters. Here H/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.
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@inproceedings{hyea2014feti-dp,
  title={FETI-DP preconditioners for a staggered discontinuous Galerkin formulation of the two-dimensional Stokes problem},
  author={Hyea Hyun Kim, Tsz Shun Eric CHUNG, and Chak Shing Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181652179970048},
  booktitle={Computers & Mathematics with Applications},
  volume={68},
  number={12},
  pages={2233-2250},
  year={2014},
}
Hyea Hyun Kim, Tsz Shun Eric CHUNG, and Chak Shing Lee. FETI-DP preconditioners for a staggered discontinuous Galerkin formulation of the two-dimensional Stokes problem. 2014. Vol. 68. In Computers & Mathematics with Applications. pp.2233-2250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181652179970048.
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