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Projection method III: Spatial discretization on the staggered grid

Authors: Weinan E and Jian-Guo Liu
Journal: Math. Comp. 71 (2002), 27-47
MSC (2000): Primary 65M06, 76M20
Published electronically: May 14, 2001
MathSciNet review: 1862987
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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.

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Additional Information

Weinan E
Affiliation: Courant Institute of Mathematical Sciences, New York, New York 10012

Jian-Guo Liu
Affiliation: Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742

Keywords: Viscous incompressible flows, projection method, numerical boundary layer, finite difference, convergence
Received by editor(s): May 19, 1997
Received by editor(s) in revised form: March 1, 2000
Published electronically: May 14, 2001
Article copyright: © Copyright 2001 American Mathematical Society