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Projection method III: spatial discretization on the staggered grid

Weinan E Courant Institute of Mathematical Sciences Jian-Guo Liu University of Maryland

Numerical Analysis and Scientific Computing mathscidoc:1702.25054

Mathematics of Computation, 71, (237), 27-47, 2002.1
In E & Liu (SIAM J Numer. Anal., 1995), we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous (we call this the semi-discrete case). In this paper, we address similar questions for the fully discrete case when the spatial variables are discretized using a staggered grid. We prove that the numerical solution in velocity has full accuracy up to the boundary, despite the fact that there are numerical boundary layers present in the semi-discrete solutions.
Viscous incompressible ows, projection method, numerical boundary layer,
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@inproceedings{weinan2002projection,
  title={Projection method III: spatial discretization on the staggered grid},
  author={Weinan E, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209111909075734384},
  booktitle={Mathematics of Computation},
  volume={71},
  number={237},
  pages={27-47},
  year={2002},
}
Weinan E, and Jian-Guo Liu. Projection method III: spatial discretization on the staggered grid. 2002. Vol. 71. In Mathematics of Computation. pp.27-47. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209111909075734384.
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