Projection method III: Spatial discretization on the staggered grid

E, Weinan; Liu, Jian-Guo

doi:10.1090/S0025-5718-01-01313-8

Projection method III: Spatial discretization on the staggered grid
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by Weinan E and Jian-Guo Liu PDF

Math. Comp. 71 (2002), 27-47 Request permission

Abstract:

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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