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Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions

Jian-Guo Liu Duke University Jie Liu National University of Singapore Robert L. Pego Carnegie Mellon University

Numerical Analysis and Scientific Computing mathscidoc:1702.25034

Chinese Annals of Mathematics, Series B, 30, (6), 743–768, 2009.11
The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C1 elements for velocity and C0 elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.
Time-dependent incompressible flowProjection methodBackward facing stepDriven cavityStokes pressureLeray projectionObtuse cornerRecycling
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@inproceedings{jian-guo2009error,
  title={Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions},
  author={Jian-Guo Liu, Jie Liu, and Robert L. Pego},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209003812292267348},
  booktitle={Chinese Annals of Mathematics, Series B},
  volume={30},
  number={6},
  pages={743–768},
  year={2009},
}
Jian-Guo Liu, Jie Liu, and Robert L. Pego. Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions. 2009. Vol. 30. In Chinese Annals of Mathematics, Series B. pp.743–768. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209003812292267348.
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