Projection method III: Spatial discretization on the staggered grid

E. Weinan; Jian Guo Liu

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

Projection method III: Spatial discretization on the staggered grid

E. Weinan, Jian Guo Liu

Mathematics

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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.

Original language	English (US)
Pages (from-to)	27-47
Number of pages	21
Journal	Mathematics of Computation
Volume	71
Issue number	237
DOIs	https://doi.org/10.1090/S0025-5718-01-01313-8
State	Published - 2002

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Keywords

Convergence
Finite difference
Numerical boundary layer
Projection method
Viscous incompressible flows

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10.1090/S0025-5718-01-01313-8

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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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AU - Liu, Jian Guo

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AB - 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.

KW - Convergence

KW - Finite difference

KW - Numerical boundary layer

KW - Projection method

KW - Viscous incompressible flows

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EP - 47

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 237

ER -

Projection method III: Spatial discretization on the staggered grid

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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